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RS Aggarwal Class 9 Solutions Chapter-14 Areas of Triangles and Quadrilaterals

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Last updated date: 27th Mar 2024
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Class 9 RS Aggarwal Chapter-14 Areas of Triangles and Quadrilaterals Solutions - Free PDF Download

RS Aggarwal Class 9 Chapter 14 Area of Triangle and Quadrilateral deals with the knowledge of the area of different types of triangles and quadrilaterals. This chapter is significant in getting an idea about the calculation of areas of important geometrical shapes like isosceles triangles, rectangles etc. Students get to know useful formulas of areas of these geometrical figures that build a foundation of engineering drawing and architecture. This chapter instills fundamental knowledge of how geometry can be implemented in solving real-life problems. The concise representation of the RS Aggarwal Solutions Class 9 Maths Chapter 14 makes it easier to grasp the concept of the chapter. The solutions can be downloaded from Vedantu’s website. 

 

Download RS Aggarwal Textbook Solutions for Class 9 Maths from Vedantu, which are curated by master teachers. Also, revise and solve the important questions for the Class 9 Maths (RS Aggarwal) exam using the updated NCERT Solutions provided by us.  Students can also avail of NCERT Solutions for Class 9 Science from our website.

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RS Aggarwal Class 9 Solutions Chapter 14 - Free PDF Download

The major concepts learned in RS Aggarwal Class 9 Maths Chapter 14 are:

  • Area of different triangles and quadrilaterals

  • Area of a quadrilaterals using diagonals

These two topics are essential in building a strong base in geometry and score well in exams. There are two exercises in the chapter:

  • The first exercise consists of 44 problems that give various cncepts of finding the area of triangles and different quadrilateral figures using suitable formulae.

  • The second exercise consists of multiple-choice questions which test the student’s grasp on the concepts learned by solving the first exercise.

The questions present in Class 9 Maths RS Aggarwal Solutions Chapter 14 are ideal for intense practice to excel in the exams.

 

The following are some important formulae that RS Aggarwal Solutions Class 9 Maths Chapter 14 comprises of:

1. The basic area of any triangle: ½  × b × h

 

where b is the base and h is the height of the triangle

 

2. Area of an equilateral triangle: An equilateral triangle is a triangle whose all the sides are equal.


Area of an equilateral triangle = \[\frac{\sqrt{3}}{4}\times a^{2}\]

 

Height of an equilateral triangle = \[\frac{\sqrt{3}}{4}\times a\]

 

where a is the measure of the two equal sides and b is the measure of the base.

 

3. Area of an isosceles triangle: \[\frac{{b}}{4}\times\sqrt{4a^{2}-b^{2}}\]

 

4. Area of a triangle having three different sides (Heron’s formula):- 

 

Suppose a triangle has sides measuring a, b and c. 

 

According to Heron’s formula:-

 

The first step includes finding the semi-perimeter of the triangle:

 

Semi-perimeter (S) = \[\frac{a+b+c}{2}\]

 

Using the above finding and implementing it in Heron’s formula for the area of a triangle constitutes the second step.

 

Area = \[\sqrt{s\lgroup s-a\rgroup\lgroup s-b\rgroup\lgroup s-c\rgroup}\]

 

On the basis of the measure of sides and angles, there are seven different types of quadrilaterals, each having a specific formula for its area.

1. Parallelogram: Its opposite sides are equal and parallel to each other.

Area of a parallelogram = base × height

 

2. Rectangle: It is a parallelogram with all four angles measuring 90⁰

Area of a rectangle = length × breadth

 

3. Square: It is a rectangle whose all sides are equal

Area of a square = side2

 

4. Rhombus: It is a parallelogram whose all sides are equal.

Area of a rhombus = base × height

 

Area of rhombus using diagonals = \[\frac{d_{1}\times d_{2}}{2}\]

 

5. Trapezium: A trapezium has one pair of sides parallel. 

Area of trapezium = \[\frac{1}{2}\lgroup a+b\rgroup\times h\]

 

where a and b are the measure of two parallel-sided and h is the height

 

6. Kite: It has two pairs of equal adjacent sides but unequal opposite sides.

Area of a kite = \[\frac{d_{1}\times d_{2}}{2}\]

 

Note: Perimeter of any figure is equal to the sum of its sides.

 

Some examples of problems are as follows:

 

Find the side and the height of an equilateral triangle whose area is 

 

100\[\sqrt{3}\] cm2

 

Ans:  Let the side be a

 

According to the problem:-

 

\[\frac{\sqrt{3}}{4}\times a^{2}=100\sqrt{3}cm^{2}\]

 

 \[a^{2}=\frac{100\sqrt{3}\times 4}{\sqrt{3}}cm^{2}\]

 

 \[a=\sqrt{400}\]

 

a = 20 cm

 

∴ Height of the triangle =  \[\frac{\sqrt{3}}{4}\times a =5\sqrt{3} cm\]

 

1. Find the Area of a Trapezoidal Pool Whose Parallel Sides are 25 m and 10 m and the Non-parallel Sides are 14 m and 13 m.

Ans:  Let the pool ABCD be divided into two figures i.e. a parallelogram and a triangle.

According to the figure, Δ BCF has sides 14m, 13m and 15m.

 

As the sides of the triangle are different, Heron’s formula will come into action.

 

S= \[\frac{14+ 15+13}{2}\] = 21 m

 

A=\[\sqrt{S\lgroup s-a\rgroup\lgroup s-b\rgroup\lgroup s-c\rgroup} = \sqrt{21\lgroup 21-14\rgroup\lgroup 21-15\rgroup\lgroup 21-13\rgroup}\] = \[\sqrt{21\times7\times6\times8} = 84m^{2}\]

 

Height of Δ BCF = Height of parallelogram AFCD

 

Area of Δ BCF = ½ × b × h = 84 m2

 

∴ ½ × 15 × h = 84 

 

h = 11.2 m

 

Area of the parallelogram AFCD = base × height = 10 × 11.2 m2 = 112 m2

 

∴ Area of the pool = (84 + 112) m2 = 196 m2

 

Tips to Prepare with RS Aggarwal Maths Class 9 Solutions Chapter 14

Vedantu’s RS Aggarwal Class 9 Maths Ch 14 Solutions are perfect for last-minute revision. In order to grow a better understanding of the chapter, one must maintain a formula list aside while going through the problems. This will give a clear picture of how to approach each and every problem with greater confidence. The solutions are designed in such a way so as to allow students to understand all the important details in the RS Aggarwal Class 9 Maths Chapter 14, enabling them to score well in the exams.

 

The experienced educators and subject experts with years of teaching experience have curated the Class 9 Maths RS Aggarwal Solutions Chapter 14 with a special focus on analytical foundation building. The Maths RS Aggarwal Class 9 Chapter 14 Solutions plays a key role in providing a better learning experience.

FAQs on RS Aggarwal Class 9 Solutions Chapter-14 Areas of Triangles and Quadrilaterals

1. How Can You Find the Area of a Rhombus Whose One Diagonal and Side Measure is Known?

In such a case the rhombus can be divided into two isosceles triangles whose measure of equal sides and base is known. The diagonal acts as the base for both the triangles.

 

Now on finding the area of each isosceles triangle using the formula: b/4 √(4a² - b²)  and adding them, one can easily find the area of the rhombus.

2. In the Case of a Right-angled Triangle, Which Side is the Height?

For a right-angled triangle, the perpendicular, which forms a 90-degree angle with the base, must be considered as the height of the triangle.

3. How Many Types of Quadrilaterals are there?

There are six different types of quadrilaterals i.e. parallelogram, rectangle, square, rhombus, trapezium, and kite.

4. Why is RS Aggarwal so important for Class 9?

RS Aggarwal is extremely important for Class 9 students as it contains detailed explanations of essential concepts that students need to learn in class 9. It also has descriptive illustrations which will aid in students’ learning. There are lots of solved examples in the RS Aggarwal book, through which students will have an idea of the practical aspects of the concepts that they learnt. Lastly, lots of unsolved questions are there in the exercises, which will help students to understand whether they have learnt or not.

5. Where do I get all the solution sets?

All the solution sets are available on the Vedantu website or app. In Vedantu, you will get solution sets, revision notes, important questions, and other useful resources. All of these have been prepared by subject experts, so students do not have to think about whether it's correct or not. These resources are available on the Vedantu website or app for free! Students just have to visit Vedantu and download the resources according to their needs.