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NCERT Solutions for Class 6 Maths Chapter 5 - Understanding Elementary Shapes

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NCERT Solutions for Class 6 Maths Chapter 5 - Understanding Elementary Shapes

In the fascinating realm of mathematics, the study of shapes forms a fundamental cornerstone. Chapter 5 of NCERT Solutions for Class 6 Maths, titled 'Understanding Elementary Shapes,' invites students on an illuminating journey into the captivating world of geometric forms and their properties. This chapter is a gateway to comprehending the basic principles of shapes, angles, and lines, which are essential not only in mathematics but also in everyday life.


Class:

NCERT Solutions For Class 6

Subject:

Class 6 Maths

Chapter Name:

Chapter 5 - Understanding Elementary Shapes

Content Type:

Text, Videos, Images and PDF Format

Academic Year:

2023-24

Medium:

English and Hindi

Available Materials:

  • Chapter Wise

  • Exercise Wise

Other Materials

  • Important Questions

  • Revision Notes


Our meticulously crafted solutions provide a comprehensive guide to mastering the intricacies of elementary shapes, enabling students to solve problems and explore the geometric wonders that surround us. Dive into this enriching chapter, where the study of shapes unveils a world of order, symmetry, and mathematical beauty, empowering young minds to grasp the language of geometry with confidence.


NCERT Solution for Class 6 Maths Chapter 5 offers a precise and accurate solution to the questions from this particular chapter. Studying it alongside the textbook will help students to improve their preparations, and score higher in their final exam.

You can also download NCERT Solution for Class 6 Science to score more in exams.

Access NCERT solutions for Class 6 Maths Chapter 5 - Understanding Elementary Shapes

Exercise 5.1

1. What is the disadvantage in comparing line segments by mere observation?

Ans: One of the main disadvantage in comparing the line segments by mere observation is that there will be high chances of miscalculation.


2. Why is it better to use a divider than a ruler, while measuring the length of a line segment?

Ans: We know that rulers are very thick. Hence, when we will measure the length, then we can misread the readings due to the thickness. Therefore, it is better to use a divider than a ruler.


3. Draw any line segment, say \[AB\]. Take any point \[C\] lying in between \[A\] and \[B\]. Measure the lengths of \[AB\], \[BC\] and \[AC\]. Is \[AB=AC+BC\]?

Ans: When we will draw any line segment $AB=7cm$ where $C$ is a point lying between $A$ and $B$ as shown in the figure below –


Line segment AB

We have $AC=3cm$ and

$BC=4cm$.

Therefore, $AB=AC+BC$

$\Rightarrow AB=3+4$

$\Rightarrow AB=7cm$.

Yes, $AB=AC+BC$.


4. If \[A,\ B,\ \text{C}\] are three points on a line such that \[AB=5cm\] , \[BC=3cm\] and \[AC=8cm\] , which one of them lies between the other two?

Ans: As, the sum of $AB$ and $BC$ is equal to the length of the line segment \[AC\]. i.e., $AC=AB+BC$

$\Rightarrow 8=5+3$.

Therefore, the point $B$ lies in between the line segment \[AC\].


5. Verify whether \[D\] is the mid-point of \[\overline{AG}\].


Line segment AG

Ans: From the figure we can observe that $AD=3cm$ and

$DG=3cm$. Therefore, $D$ is the mid-point.


6. If \[B\] is the mid-point of \[AC\] and \[C\] is the mid-point of \[BD\], where \[A\], \[B\], \[C\], \[D\] lie on a straight line, say why \[AB=CD\] ?

Ans:


Straight Line AD

As, given we have $B$ is the midpoint of $AC$.

$\Rightarrow AB=BC$

Similarly, $C$ is the midpoint of $BD$.

$\Rightarrow BC=CD$

From, the above conditions, we have $\Rightarrow AB=CD$. Hence, proved.


7. Draw five triangles and measure their sides. Check in each case, of the sum of the lengths of any two sides is always less than the third side.

Ans: No, from the given figures below we can conclude that the sum of two sides of a triangle can never be less than the third side of that triangle.


Five triangle


Exercise 5.2

1. What fraction of a clockwise revolution does the hour hand of a clock turn through, 

(i) when it goes from \[3\] to \[9\].

Ans: When the hour hand of a clock goes from $3$ to $9$, the number of divisions between them will be $6$, so the fraction will be $\frac{6}{12}=\frac{1}{2}$.


(ii) when it goes from \[4\] to \[7\].

Ans: When the hour hand of a clock goes from $4$ to $7$, the number of divisions between them will be $3$, so the fraction will be $\frac{3}{12}=\frac{1}{4}$.


(iii) when it goes from \[7\] to \[10\].

Ans: When the hour hand of a clock goes from $7$ to $10$, the number of divisions between them will be $3$, so the fraction will be $\frac{3}{12}=\frac{1}{4}$.


(iv) when it goes from \[12\] to \[9\].

Ans: When the hour hand of a clock goes from $12$ to $9$, the number of divisions between them will be $9$, so the fraction will be $\frac{9}{12}=\frac{3}{4}$.


(v) when it goes from \[1\] to \[10\].

Ans: When the hour hand of a clock goes from $1$ to $10$, the number of divisions between them will be $9$, so the fraction will be $\frac{9}{12}=\frac{3}{4}$.


(vi) when it goes from \[6\] to \[3\].

Ans: When the hour hand of a clock goes from $6$ to $3$, the number of divisions between them will be $9$, so the fraction will be $\frac{9}{12}=\frac{3}{4}$.


2. Where will the hand of a clock stop if it:

(a) starts at \[12\] and make \[\frac{1}{2}\] of a revolution, clockwise?

Ans: When the hand of a clock starts at $12$ and make $\frac{1}{2}$ of a revolution, clockwise then it will stop at $\frac{12}{2}=6$.


(b) starts at \[2\] and makes \[\frac{1}{2}\] of a revolution, clockwise?

Ans: When the hand of a clock starts at $2$ and make $\frac{1}{2}$ of a revolution, clockwise then it will stop at $2+\frac{12}{2}=8$.


(c) starts at \[5\] and makes \[\frac{1}{4}\] of a revolution, clockwise?

Ans: When the hand of a clock starts at $5$ and make $\frac{1}{4}$ of a revolution, clockwise then it will stop at $5+\frac{12}{4}=8$.


(d) starts at \[5\] and makes \[\frac{3}{4}\] of a revolution, clockwise?

Ans: When the hand of a clock starts at $5$ and make $\frac{3}{4}$ of a revolution, clockwise then it will stop at $5+12\times \frac{3}{4}=14$ i.e., at $2$ as one revolution is $=12$.


3. Which direction will you face if you start facing:

(a) East and make \[\frac{1}{2}\] of a revolution clockwise?

Ans:


Clockwise from east

When we will make $\frac{1}{2}$ of a revolution, clockwise from east, then we will face the west direction.


(b) East and make \[1\frac{1}{2}\] of a revolution clockwise?

Ans: When we will make $1\frac{1}{2}$ of a revolution, clockwise from east, then we will face the west direction.


(c) West and makes \[\frac{3}{4}\] of a revolution clockwise?

Ans:


Clockwise from west

When we will make $\frac{3}{4}$ of a revolution, clockwise from west, then we will face the north direction.


(d) South and make one full revolution?

Ans:


Revolution from south

When we will make a one full revolution from south, then we will face the south direction. There will be no need for mentioning clockwise or anti-clockwise because anyhow one full revolution will bring us back to the original direction.


4. What part of a revolution have you turned through if you stand facing –

(a) East and turn clockwise to face north?

Ans:


Clockwise from east to face north

When we will turn clockwise from east to face north, then the revolution will be $\frac{3}{4}$.


(b) South and turn clockwise to face east?

Ans:


Clockwise from south to face east

When we will turn clockwise from south to face east, then the revolution will be $\frac{3}{4}$.


(c) West and turn clockwise to face east?

Ans:


Hour hand of a clock from 3 to 6


When we will turn clockwise from west to face east, then the revolution will be $\frac{1}{2}$.


5. Find the number of right angles turned through by the hour hand of a clock 

(a) when it goes from \[3\] to \[6\].

Ans: When the hour hand of a clock goes from $3$ to $6$ then the number of right angles turned will be one.


Hour hand of a clock from 2 to 8


(b) when it goes from \[2\] to \[8\].

Ans: When the hour hand of a clock goes from $2$ to $8$ then the number of right angles turned will be two.


Hour hand of a clock from 5 to 11


(c) when it goes from \[5\] to \[11\].

Ans: When the hour hand of a clock goes from $5$ to $11$ then the number of right angles turned will be two.


Hour hand of a clock from 10 to 1


(d) when it goes from \[10\] to \[1\].

Ans: When the hour hand of a clock goes from $10$ to $1$ then the number of right angles turned will be one.


Hour hand of a clock from 12 to 9


(e) when it goes from \[12\] to \[9\].

Ans: When the hour hand of a clock goes from $12$ to $9$ then the number of right angles turned will be three.


Hour hand of a clock from 12 to 6


(f) when it goes from \[12\] to \[6\].

Ans: When the hour hand of a clock goes from $12$ to $6$ then the number of right angles turned will be two.


South to west in clockwise direction

6. How many right angles do you make if you start facing –

(a) South and turn clockwise to west?

Ans: When we start facing south and turn clockwise to west then the number of right angles turned will be one.


North to east in anti-clockwise direction

(b) North and turn anti-clockwise to east?

Ans: When we start facing north and turn anti-clockwise to east then the number of right angles turned will be three.


West to east direction

(c) West and turn to west?

Ans: When we start facing west and turn to west then the number of right angles turned will be four.


South to north direction

(d) South and turn to north?

Ans: When we start facing south and turn to north then the number of right angles turned will be two.


Clock pointing at 6 and 9

7. Where will the hour hand of a clock stop if it starts: 

(a) from \[6\] and turns through \[1\] right angle?

Ans: One right angle = One-fourth of complete rotation of a clock $\frac{1}{4}\times 12=3$

When the hour hand of a clock starts from $6$ and turns through $1$ right angle, then it will stop at $6+3=9$.


Clock pointing at 8 and 2

(b) from \[8\] and turns through \[2\] right angles?

Ans: One right angle = One-fourth of complete rotation of a clock $\frac{1}{4}\times 12=3$

When the hour hand of a clock starts from $8$ and turns through $2$ right angles, then it will stop at $8+3+3=14$ i.e., at $2$.


Clock pointing at 10 and 7

(c) from \[10\] and turns through \[3\] right angles?

Ans: One right angle = One-fourth of complete rotation of a clock $\frac{1}{4}\times 12=3$

When the hour hand of a clock starts from $10$ and turns through $3$ right angles, then it will stop at $10+3+3+3=19$ i.e., at 7$.


Clock pointing at 7

(d) from \[7\] and turns through \[2\] straight angles?

Ans: One Straight angle = 2 right angles

When the hour hand of a clock starts from $7$ and turns through $2$ straight angles, then it will stop at $7+6+6=19$ i.e., at 7.


Acute Angle


Exercise 5.3

1. Match the following:

(i) Straight angle     

(a) less than one-fourth a revolution 

(ii) Right angle 

(b) more than half a revolution

(iii) Acute angle 

(c) half of a revolution 

(iv) Obtuse angle  

(d) one-fourth a revolution

(v) Reflex angle 

(e) between \[\frac{1}{4}\] and \[\frac{1}{2}\] of a revolution 



(f) one complete revolution

 

Ans:

(i) Straight angle

(c) half of a revolution

(ii) Right angle

(d) one-fourth a revolution

(iii) Acute angle

(a) less than one-fourth a revolution

(iv) Obtuse angle

(e) between $\frac{1}{4}$ and $\frac{1}{2}$ of a revolution


(v) Reflex angle

(b) more than half a revolution


2. Classify each one of the following angles as right, straight, acute, obtuse or reflex:

(a) 

obtuse angle

Ans: It is an acute angle.


(b) 

right angle

Ans: It is an obtuse angle.


(c)

reflex angle

Ans: It is a right angle.


(d)

straight angle

Ans: It is a reflex angle.


(e)

acute angle

Ans: It is a straight angle.


(f) 

angle to find (acute)

Ans: It is an acute angle.


Exercise 5.4

1. What is the measure of –

(i) a right angle?

Ans: The measure of a right angle is $90{}^\circ $.


(ii) a straight angle?

Ans: The measure of a straight angle is $180{}^\circ $.


2. Say True or False:

(a) The measure of an acute angle \[<90{}^\circ \].

Ans: True.

As, we measure any acute angle, then it will always be less than a right angle.


(b) The measure of an obtuse angle \[<90{}^\circ \].

Ans: False.

When we measure an obtuse angle, then it will always be more than a right angle.


(c) The measure of a reflex angle \[>180{}^\circ \].

Ans: True.

A reflex angle is always more than the measure of a straight line.


(d) The measure of a complete revolution \[=360{}^\circ \].

Ans: True.

When we complete one revolution, it is measured as turn of two straight lines.


(e) If \[m\angle A=53{}^\circ \] and 

\[m\angle B=35{}^\circ \], then 

\[m\angle A>m\angle B\].

Ans: True.


3. Write down the measure of:

(a) some acute angles

Ans: As, an acute angle is measured as less than a right angle. Therefore, some of the acute angles will be $45{}^\circ $, $30{}^\circ $, and etc.


(b) some obtuse angles

Ans: As, an obtuse angle is measured as more than a right angle. Therefore, some of the obtuse angles will be $105{}^\circ $, $140{}^\circ $, and etc.


4. Measure the angles given below, using the protractor and write down the measure:

(a)

figure obtuse

Ans: After using the protractor, we can conclude that the given figure is an acute angle measured as $40{}^\circ $.


(b)

find angle right angle

Ans: After using the protractor, we can conclude that the given figure is an obtuse angle measured as $130{}^\circ $.


(c) 

find figure acute angle

Ans: After using the protractor, we can conclude that the given figure is a right angle measured as $90{}^\circ $.


(d)

find greater angle

Ans: After using the protractor, we can conclude that the given figure is an acute angle measured as $60{}^\circ $.


5. Which angle has a large measure? First estimate and then measure:


find angle great

Ans: After estimating we can conclude that the measure of angle $B$ is larger than the measure of angle $A$.

Measure of angle \[A=\]

The measure of angle $A$ is $40{}^\circ $.

Measure of angle \[B=\]

The measure of angle $B$ is $65{}^\circ $.


6. From these two angles which has larger measure? Estimate and then confirm by measuring them –


estimating angle

Ans: From the given figure we can estimate that the second angle has a larger measure than the first angle. After using the protractor, the measure of first angle is $45{}^\circ $ and the measure of second angle is $60{}^\circ $.


7. Fill in the blanks with acute, obtuse, right, or straight: 

(a) An angle whose measure is less than that of a right angle is __________.

Ans: An angle whose measure is less than that of a right angle is acute angle.


(b) An angle whose measure is greater than that of a right angle is __________. 

Ans: An angle whose measure is greater than that of a right angle is obtuse angle.


(c) An angle whose measure is the sum of the measures of two right angles is __________. 

Ans: An angle whose measure is the sum of the measures of two right angles is straight angle.


(d) When the sum of the measures of two angles is that of a right angle, then each one of them is __________. 

Ans: When the sum of the measures of two angles is that of a right angle, then each one of them is acute angle.


(e) When the sum of the measures of two angles is that of a straight angle and if one of them is acute then the other should be ___________.

Ans: When the sum of the measures of two angles is that of a straight angle and if one of them is acute then the other should be obtuse angle.


8. Find the measure of the angle shown in each figure. (First estimate with your eyes and then find the actual measure with a protractor).


find the in the clock

Ans: After estimating the measure of each angle shown in figure, we have –

(i) $30{}^\circ $

(ii) $120{}^\circ $

(iii) $60{}^\circ $

(iv) $150{}^\circ $


9. Find the angle measure between the hands of the clock in each figure:


angle 30

Ans: From the given figure, as the revolution is of $\frac{1}{4}$ from $9$ to $12$ hence, the measure of the angle in first figure will be of $90{}^\circ $, second figure has angle of measure $30{}^\circ $ as each division is equal and the third figure has angle of measure $180{}^\circ $ as the revolution is of $\frac{1}{2}$ which will form a straight line.


10. Investigate:

In the given figure, the angle measure \[30{}^\circ \]. Look at the same figure through a magnifying glass. Does the angle become larger? Does the size of the angle change?


measure nd classify angle

Ans: No, the size of the angle does not change and hence, remains same even after using the magnifying glass.


11. Measure and classify each angle:


angle table

Ans: The measure of each angle can be measured by the help of a protractor. Hence, the angles will be –


measure the angle

Exercise 5.5

1. Which of the following are models for perpendicular lines –

(a) The adjacent edges of a tabletop.

Ans: Yes, adjacent edges of a table top are perpendicular.


(b) The lines of a railway track.

Ans: No, the lines of a railway track are not perpendicular.


(c) The line segments forming the letter ‘\[L\]’.

Ans: Yes, the line segments forming the letter $L$ are perpendicular.


(d) The letter \[V\].

Ans: No, the letter $V$ is not perpendicular.


2. Let \[PQ\] be the perpendicular to the line segment \[XY\]. Let \[PQ\] and \[XY\] intersect in the point \[A\]. What is the measure of \[\angle PAY\].

Ans: As, $PQ$ and $XY$ are perpendicular line segments to each other and intersect at point $A$ can be shown in the figure below –


perpendicular to line

Therefore, the measure of $\angle PAY=90{}^\circ $.


3. There are two “set-squares” in your box. What are the measures of the angles that are formed at their corners? Do they have any angle measure that is common?

Ans: From the two “set-squares” in our box, we have one set-square as $30{}^\circ $, $60{}^\circ $, $90{}^\circ $ and another set-square as $45{}^\circ $, $45{}^\circ $, $90{}^\circ $. Therefore, the angle that is common is $90{}^\circ $.


4. Study the diagram. The line \[l\] is perpendicular to line \[m\].


nature of angle

(a) Is \[CE=EG\]?

Ans: As, $CE=2\ \text{units}$ and

$EG=2\ \text{units}$. Therefore, 

$CE=EG$.


(b) Does \[PE\] bisect \[CG\]?

Ans: From the given figure we can conclude that yes, $PE$ bisects $CG$.


(c) Identify any two-line segments for which \[PE\] is the perpendicular bisector.

Ans: Any two-line segments for which $PE$ is the perpendicular bisector are $DF$ and $CG$.

(d) Are these true? 

(i) \[AC>FG\]

Ans: Yes, it’s true. As, $AC=2\ \text{units}$ and

$FG=1\ \text{unit}$. Hence, $AC>FG$.


(ii) \[CD=GH\]

Ans: Yes, it’s true. As, both $CD$ and $GH$ are of $\text{1}\ \text{unit}$.


(iii) \[BC<EH\]

Ans: Yes, it’s true. As, $BC=1\ unit$ and

$EH=3\ \text{units}$. Hence, $BC<EH$.


Exercise 5.6

1. Name the types of following triangles: 

(a) Triangle with lengths of sides \[7cm\], \[8cm\] and \[9cm\].

Ans: As, all the three sides of the triangle have different lengths,

therefore, it is a scalene triangle.


(b) \[\Delta ABC\] with \[AB=8.7cm\],  \[AC=7cm\] and \[BC=6cm\].

Ans: As, all the three sides of the triangle have different lengths, therefore, it is a scalene triangle.


(c) \[\Delta PQR\] such that \[PQ=QR=PR=5cm\].

Ans: As, all the three sides of the triangle have same lengths, therefore, it is an equilateral triangle.


(d) \[\Delta DEF\] with \[m\angle D=90{}^\circ \].

Ans: Since, one of the angles of the triangle is $90{}^\circ $, therefore, it is a right-angled triangle.


(e) \[\Delta XYZ\] with \[m\angle Y=90{}^\circ \] and  \[XY=YZ\].

Ans: Since, one of the angles of the triangle is $90{}^\circ $, and two sides are of same length therefore, it is an isosceles right-angled triangle.


(f) \[\Delta LMN\] with \[m\angle L=30{}^\circ \], \[m\angle M=70{}^\circ \] and  \[m\angle N=80{}^\circ \].

Ans: Since, all the angles of the triangle are less than right angle, therefore, it is an acute triangle.


2. Match the following: Measure of Triangle Types of Triangle 

(i) \[3\] sides of equal length

(a) Scalene

(ii) \[2\] sides of equal length 

(b) Isosceles right angle 

(iii) All sides are of different length   

(c) Obtuse angle

(iv) \[3\] acute angles   

(d) Right angle 

(v) \[1\] right angle   

(e) Equilateral 

(vi) \[1\] obtuse angle    

(f) Acute angle

(vii) \[1\] right angle with two sides  

(g) Isosceles of equal length


Ans:

(i) \[3\] sides of equal length

(e) Equilateral 

(ii) \[2\] sides of equal length 

(g) Isosceles of equal length

(iii) All sides are of different length   

(a) Scalene

(iv) \[3\] acute angles   

(f) Acute angle

(v) \[1\] right angle   

(d) Right angle 

(vi) \[1\] obtuse angle    

(c) Obtuse angle

(vii) \[1\] right angle with two sides  

(b) Isosceles right angle


3. Name each of the following triangles in two different ways: (You may judge the nature of angle by observation).


match stck triangle

Ans: The triangles in two different ways will be as –

(a) Acute angled triangle and Isosceles triangle.

(b) Right-angled triangle and Scalene triangle.

(c) Obtuse-angled triangle and Isosceles triangle.

(d) Right-angled triangle and Isosceles triangle.

(e) Equilateral triangle and acute angled triangle.

(f) Obtuse-angled triangle and scalene triangle.


4. Can you make a triangle with

(a) \[3\] matchsticks – Triangle possible


match stik sq

(b) \[4\] matchsticks – Triangle not-possible


angle matchsticks

(c)  \[5\] matchsticks – Triangle Possible 

This is an acute angle triangle, and it is possible to make triangle with five matchsticks.


matchstick tri-06

(d) \[6\] matchsticks – Triangle Possible


polygon

Exercise 5.7

1. Say true or false: 

(a) Each angle of a rectangle is a right angle.

Ans:

True. Each side of a rectangle is a right angle.


(b) The opposite sides of a rectangle are equal in length.

Ans:

True. Opposite sides of a rectangle are always equal and parallel to each other.


(c) The diagonals of a square are perpendicular to one another.

Ans:

True. Square has diagonals that are bisecting each other at $90{}^\circ $.


(d) All the sides of a rhombus are of equal length.

Ans:

True. Rhombus has all sides of equal length.


(e) All the sides of a parallelogram are of equal length.

Ans:

False. Not all sides of a parallelogram are of equal length.


(f) The opposite sides of a trapezium are parallel.

Ans: False. Opposite sides of a trapezium are never equal.


2. Give reasons for the following: 

(a) A square can be thought of as a special rectangle.

Ans: As, opposite sides of a rectangle are equal, and all angles are $90{}^\circ $. Therefore, we can say square as a special rectangle with all sides of equal length and all angles as $90{}^\circ $.


  1. A rectangle can be thought of as a special parallelogram.

Ans: As, both rectangle and parallelogram have opposite sides equal and parallel to each other. Therefore, we can say that rectangle can be a special parallelogram.


(c) A square can be thought of as a special rhombus.

Ans: Because both square and rhombus has all sides of same length and also their diagonals bisect each other at $90{}^\circ $. Therefore, a square can be a special rhombus.


(d) Squares, rectangles, parallelograms are all quadrilateral.

Ans: A quadrilateral is a shape that has at least $4$ sides. Therefore, squares, rectangles, parallelograms are all types of quadrilaterals.


(e) Square is also a parallelogram.

Ans: Since, in parallelogram opposite sides are always equal and parallel to each other. Therefore, a square can also be a special parallelogram.


3. A figure is said to be regular if its sides are equal in length and angles are equal in measure. Can you identify the regular quadrilateral?

Ans: A square has its all sides in equal length and all angles are also equal. Therefore, a square is a regular quadrilateral.


Exercise 5.8

1. Examine whether the following are polygons. If anyone among these is not, say why?


name polygon

Ans: As, the figure in $(a)$ is not close, hence, it cannot be a polygon. Whereas figure $(b)$ is a closed shape, hence, it is a polygon. Similarly, in figure $(c)$ and $(d)$ as the shape is not enclosed by line segments, therefore, they are also not polygons.


2. Name each polygon:


Regular hexagon

Ans: The polygon in figure $(a)$ is a quadrilateral as it has four sides, in figure $(b)$ it is a triangle as it has three sides, in figure $(c)$ it is a pentagon as it has five sides and in figure $(d)$ it is a octagon as it has eight sides.


3. Draw a rough sketch of a regular hexagon. Connecting any three of its vertices, draw a triangle. Identify the type of the triangle you have drawn.

Ans: A rough sketch of a regular hexagon with connecting any three of its vertices and drawing a triangle will be as –


Regular octagon

So, we have joined three vertices $A$, $E$, and $F$. Therefore, the triangle formed is an isosceles triangle as two sides are equal.


4. Draw a rough sketch of a regular octagon. (Use squared paper if you wish). Draw a rectangle by joining exactly four of the vertices of the octagon.

Ans: A rough sketch of a regular octagon when a rectangle is drawn using any of its four vertices will be as –


Regular pentagon

Here, $CDGH$ is a rectangle.


5. A diagonal is a line segment that joins any two vertices of the polygon and is not a side of the polygon. Draw a rough sketch of a pentagon and draw its diagonals.

Ans: A rough sketch of a pentagon with its diagonals will be as –


Cone

Here, $ABCDE$ is a pentagon which has diagonals as $AD$, $AC$, $BE$, and $BD$.


Exercise 5.9

1. Match the following: 

(a) Cone                                                           


Sphere

(b) Sphere                                                      

 

Cylinder

(c) Cylinder                              


Cuboid

(d) Cuboid                                                    

   

Pyramid

(e) Pyramid     

                                              

Cone

Give two example of each shape.

Ans:

(a) Cone   

                                                        

Sphere

Examples are birthday caps, ice-cream cone, etc

(b) Sphere        

                                              

Cylinder

Examples are ball, orange, etc.


(c) Cylinder                                                      


Cuboid

Examples are bottles, cylinder, etc.


(d) Cuboid                                                     


Pyramid

Examples are books, geometry box, etc.


(f) Pyramid                                             

seo images

Examples are tent, tower, etc.


2. What shape is: 

(a) Your instrument boxes?

Ans: Instrument boxes are of cuboid shape.


(b) A brick?

Ans: A brick is cuboid shaped.


  1. A match box?

Ans: A match box has shape of a cuboid.


  1. A road-roller?

Ans: Road roller has cylindrical shape.


  1. A sweet laddu?

Ans: A sweet laddu is of spherical shape.


NCERT Solutions for Class 6 Maths Chapter 5 - Understanding Elementary Shapes

NCERT Solutions Class 6 Maths Chapter 5 – Free PDF Download

Chapter 5 of Class 6 Mathematics discusses various shapes that exist in the world around us. It is imperative for students to have a clear understanding of different geometrical shapes, and this solution helps them in this process.

This chapter has a total of ten topics, and each of them tackles a different concept. It begins with the measurement technique of different line segments and then moves into more advanced concepts of angles and various geometrical shapes.

NCERT Solutions for Class 6 Maths Chapter 5 are a vital study material for students of class six. It offers comprehensive yet easy to understand insight into this important concept of mathematics. It helps students to comprehend the topics quickly and improve their exam preparations.


NCERT Solution for Class 6 Maths Chapter 5 Topic-Wise Discussion

Class 6 Maths chapter 5 has ten sub-topics, and here is a brief idea of each topic –

1. Introduction

The chapter begins with an introduction to various geometric shapes and how they are created with different lines. It talks about how shapes use straight lines, curved lines, etc. This chapter allows a more in-depth Understanding of Elementary shapes Class 6 with real-life examples.


2. Measuring Line Segment

A line segment is a portion of any lines that one can draw. In this chapter, students will learn how to measure different types of lines and tools necessary for the job. Along with that, they will also learn how to compare between various line segments in this chapter of NCERT Class 6 Maths Chapter 5.


3. Angles – Right and Straight

The next sub-topic in this NCERT Maths Book Class 6 Chapter 5 solutions talks about a vital concept of geometry, angles. In this particular section, students learn about two important angles, right-angle and straight-angle.

A right-angle is of 90 degrees, and a straight-angle is of 180 degrees. There are various examples of directions and the position of clock hands to make this concept clear to the students.


4. Angles – Acute, Obtuse, Reflex

Apart from right-angle and straight-angle, there are three primary classifications of angles, these are –

  • Acute angle, which is less than the right-angle.

  • Obtuse angle, which is higher than a right-angle but lower than a straight-angle.

  • Reflex angle, which is higher than a straight-angle.

The fourth section of NCERT Class 6 Maths Chapter 5 provides a detailed look into these three angles. There are various real-life examples to make these concepts more relatable to the students.


5. Measuring Angles

Class 6 Understanding Elementary Shapes further includes the discussion of angle measurement. In this section, students will learn how to measure various angles effectively. They will learn the use of a protractor, and how it helps in accurate measurement of different angles.


6. Perpendicular Lines

When two lines intersect each other at a right angle, they are called perpendicular lines. The next chapter of Elementary Shapes Class 6, includes a detailed discussion of this topic.


7. Classification of Triangles

In this sub-topic of NCERT Solutions for Class 6 Maths Chapter 5, candidates will know in detail about various triangles. Along with their properties, students will also learn how to name triangles based on their sides and the degree of their angles. 

This section includes an introduction to types of triangles like scalene, isosceles, equilateral, etc. named as per the sides of a triangle. Along with them, students will also learn about different triangle names based on their angle size like a right-angle triangle, obtuse-angled triangle, acute-angle triangle, etc.


8. Quadrilaterals

A quadrilateral is nothing but a polygon with four sides. However, there is more to that, and in this Class 6th Maths Chapter 5 students will know about it in detail. Students can use the set-squares to form various quadrilaterals.


9. Polygon

Class 6 Maths Understanding Elementary Shapes further discusses the concept of a polygon in its next section. A triangle and a quadrilateral is also a polygon with 3 and 4 sides respectively. In this particular discussion, students will come across other polygon types like pentagon, hexagon, and octagon. There are a few real-life examples of polygon resented as well in this chapter, to help students understand.


10. Three-Dimensional Shapes

Lastly, the CBSE Class 6 Maths Chapter 5 includes a discussion about 3-D shapes. Students have already studied about 2-D shapes till now, but now they will move on to more advanced concepts. These three-dimensional shapes are everywhere in the surroundings, and the use of them as an example helps students to comprehend such complicated topics easily.

It also includes an extensive discussion on the number of edges, faces, and vertices 3-D figures have.


We Cover All Exercises In The Chapter Given Below

EXERCISE 5.1 - 7 Questions with Solutions

EXERCISE 5.2 - 7 Questions with Solutions

EXERCISE 5.3 - 2 Questions with Solutions

EXERCISE 5.4 - 11 Questions with Solutions

EXERCISE 5.5 - 4 Questions with Solutions

EXERCISE 5.6 - 4 Questions with Solutions

EXERCISE 5.7 - 3 Questions with Solutions

EXERCISE 5.8 - 5 Questions with Solutions

EXERCISE 5.9 - 2 Questions with Solutions.


Know the Reasons to Study NCERT Solution Class 6 Maths Chapter 5

Here are some prominent reasons why NCERT Solutions for Class 6 Maths Chapter 5 is a must-read for students –

  • These NCERT solutions follow the curriculum drafted by CBSE. Thus, their answers are in accordance with the requirements of CBSE.

  • The language used here is simple and easy to understand. Hence, it is easier for students to comprehend any topic.

  • The solutions provided in Chapter 5 Maths Class 6 NCERT Solutions are detailed, which will help students to gather all the necessary information.

  • Additionally, the use of practical examples makes things easy to understand for students.

NCERT Solutions for Class 6 Maths Chapter 5 are readily available online for free. Students can download it from the website of Vedantu.

Conclusion 

Vedantu's NCERT Solutions for Class 6 Maths Chapter 5 - "Understanding Elementary Shapes" provide an essential resource for young learners. These solutions are thoughtfully designed to align seamlessly with the NCERT curriculum, ensuring that students receive clear explanations and step-by-step guidance in understanding geometric concepts. By offering practical insights into elementary shapes, these solutions empower students to grasp the fundamentals of geometry effectively. Vedantu's commitment to quality education shines through in these solutions, making them a crucial tool for Class 6 students. By utilizing these NCERT Solutions, students can strengthen their mathematical skills, develop spatial reasoning abilities, and foster a solid foundation in geometry, all of which are essential for their academic growth.

FAQs on NCERT Solutions for Class 6 Maths Chapter 5 - Understanding Elementary Shapes

1. How to get a better understanding of chapter 5 Understanding Elementary Shapes?

Understanding the concept of various shapes is important to excel in sections of mathematics like geometry and trigonometry. The analysis of line, angle, and the theories associated with them are essential for higher studies. The best way to get a clear understanding of these concepts is via NCERT solutions. It offers the necessary guidance to the students on how to solve the questions and learn these concepts effectively.

2. What is the meaning of Understanding Elementary Shapes?

It means the development of tools for the measurement of shapes and their sizes. All the elementary shapes can be formed using lines and curves. We can organize each of them into triangles, line segments, angles, polygons, and circles, and the most important thing is that they have different measures of shapes and sizes. To understand the elementary shapes more clearly, we should have some idea about types of angles, triangles, quadrilaterals, polygons, polyhedrons, etc.

3. What are parallelograms?

A parallelogram is a geometrical shape in which two sides are parallel to each other. If it is a four-sided figure, it is called quadrilateral and the parallel sides are equal in length. The interior opposite angles of a parallelogram are equal in measure. The sum of adjacent angles of a parallelogram is equal to 180 degrees. For example, square and rectangular are parallelograms.

4. How do you study practical geometry?

Practical geometry is an easy subject. Students can practice practical geometry using tools such as a ruler, protractor, compass, etc. Students have to follow the steps for making different figures. They can follow the instructions given for NCERT Solutions Class 6 Maths on the internet. Vedantu is the best online learning website for students of all classes because all NCERT Solutions are given in simple and easy language. These solutions are available on Vedantu’s official website (vedantu.com) and mobile app free of cost.

5. What are the disadvantages of comparing line segments by tracing and by observation?

The disadvantage in comparing the line segments by tracing and by observation is that there is a higher chance of error while observing the line segment. When we have to compare the line segment of almost the same length there is a high chance of uncertainty about which one is longer. Thus, it is not the appropriate way to compare the line segments having almost the same length. We can conclude tracing is a better way to compare line segments.

6. What are different types of parallelograms?

Different types of parallelograms are:

  • Square: It is a four-sided figure in which all sides are equal and all angles are equal to 90 degrees. The diagonals are equal.

  • Rectangle: It is also a four-sided figure in which opposite sides are equal and all angles are equal to 90 degrees. The diagonals are equal.

  • Rhombus: It is also a four-sided figure in which all sides are equal.