Area and Its Boundary Class 5 Notes: CBSE Maths Chapter 11

What is a 2D figure?

• A two-dimensional shape is a plane figure that can be drawn on a flat surface.

• It has only two dimensions which are length and width. It has no thickness or depth

• Example: Rectangle, Circle, Square, etc

What is Area?

• The space enclosed by a plane figure is referred to as its area (2 Dimensional shapes). 

• Square units are used to measure area. 

• The area of a plane figure is the number of squares required to completely cover it. Example: The area of the square given below will be the number of squares of the unit side required to completely cover the square.

Area of big Square

Since it would be silly to always count all those squares  to find the area       we just multiply both sides.

• Hence we can get formulae for the area as 

Area of Rectangle and Square

• Formula to find the number of figures of area “x” to completely cover a figure of area “y” = y/x. 

Example : No of pink sheets required to completely cover yellow sheet will be 18/3 = 6

Area of Rectangle

Solved Example

Question 1. If the length of the board is 12 cm and the breadth is 10 cm and we want to cover the board with square sheets. The side of the square sheet is 2 cm. How many sheets are required to cover the board?

Solution: Length of board = 12 cm 

Breath of board = 10 cm

Area of board = length x breadth

⇒ Area of board = (10 x 12) cm2

⇒ Area of board = 120 cm2

Side of sheet = 2 cm

 Area of sheet =side × side

⇒ Area of sheet= (2 × 2) cm2

⇒ Area of sheet = 4 cm2

Number of sheets required = Area of board / Area of sheet

⇒ Number of sheets required = 120 / 4 

⇒ Number of sheets required = 30

Answer. 30 sheets are required to cover the board.

What is Perimeter?

• The perimeter of a two-dimensional figure is the length of the figure's boundary.

• If the figure is a triangle, square, or rectangle, the perimeter is the sum of the edge lengths.

• Example: Let’s find the perimeter of a given rectangle

Perimeter of Rectangle

Here the length of the rectangle is 25 m whereas the breadth of the rectangle is 5 m. Length of the boundary will be (25 + 5 + 25 + 5) m = 2(25 + 5)m = 60 m.

• Hence, we get formulae for perimeter as :

Perimeter of Rectangle and Square

Solved Example

Question 2. It is known that the area of a square is 81 cm2. Find the perimeter of the square.

Solution: Area =81 cm2

Area = side × side

⇒ 81= (a)2

⇒ (9)2 = (a)2

⇒ 9 cm = a

⇒ Perimeter = 4 × side

⇒ Perimeter = 4 × 9

⇒ Perimeter = 36 cm 

Answer. The perimeter of the given square is 36 cm.

Units

• A unit of measurement is a definite magnitude of a quantity that is adopted by law and is used as a standard for measuring the same type of quantity.

• We measure the perimeter of any figure in mm, cm, m, or km.

• We measure the area of any figure in mm square, cm square, m square, or km square.

Measurement Abbreviations and their comparisons

1 mm < 1 cm < 1 m < 1 km

• 1 mm2 < 1 cm2 < 1 m2 < 1 km2

Scale of drawing 

• A drawing of a real object reduced or enlarged by a certain amount (called the scale).

• Example: A garden with a paved border is shown below. 1 cm on this garden is equal to 100 m on the ground. 

Rectangular garden

Let’s find the length and breadth of the garden on the ground.

Length will be 6 x 100 m = 600 m.

Breadth will be 5 x 100 m = 500 m.

Relationship between area and perimeter

• Consider two rectangles A and B having the same perimeter as 18 units.

Relationship between area and perimeter

Observe that both of them have different areas (Area of Rectangle A = 18 square units whereas Area of Rectangle B is 20 square units)

Relationship between area and perimeter of a rectangle

Hence we conclude that:

•  The two shapes having the same perimeter can have different areas. 

• Similarly, two shapes having the same areas can have different perimeters.

Area when we cut image

• If we cut any 2D figure then the area of that 2D figure will be equal to the area of pieces. For example, if we cut a polygon into three pieces then the area of the polygon is equal to the sum of the area of three pieces.

Area when we cut the image

Solved Example

Question 3. Take a sheet of paper with a length of 14 cm and a breadth of 5 cm. Now cut this sheet into 5 equal rectangles. Find the area of each smaller rectangle.

Solution: Area of a sheet of length 14 cm and breadth 5 cm = Sum of the area of five equal rectangles

Area of the big rectangle 

Area of sheet of length 14 cm and breadth 5 cm = 5 x (area of small rectangle)

⇒ 14 x 5 = 5 x (area of small rectangle)

⇒ Area of small rectangle = (14 x 5) / 5 

⇒ Area of small rectangle = 14 cm2

Answer. The area of each smaller rectangle is 14 cm2.

Area of irregular shapes

Area of irregular shapes

Question 4. Find the area of the below figure:

Solution: After colouring and counting we observe that the total area of the figure will be (3+7+1) square units = 11 square units. 

Practice Questions for Your Understanding

Question 1. Umang plans to tile his kitchen floor with grey square tiles. Each side of the tile is 10 cm. His kitchen is 200 cm in length and 150 cm wide. How many tiles will he need?

Question 2. Rahul, Bhavika, and Kabir made rectangular greeting cards. Complete the table for their cards: 

Question 3. Find the area of the below figure: 

Answer 1. 300 tiles. 

Answer 2. 

Answer 3. 7 square units

Hint:       

5 Important Topics of Class 5 Maths Chapter 11 Area and its Boundary

Importance of Maths Chapter 11 Area and its Boundary Class 5 Notes PDF

• Revision notes help us quickly understand and remember key concepts before exams.

• They save time by focusing on essential information and skipping unnecessary details.

• These notes simplify complex topics, making them easier to understand and use.

• They provide practical examples that show how theoretical knowledge is used in real-life situations.

• They increase confidence by clearly understanding what to expect in exams.

Tips for Learning the Chapter 11 Area and its Boundary Class 5 Notes

• Understand the concept of area and perimeter clearly with simple examples.

• Practice calculating the area and perimeter of regular shapes like squares and rectangles.

• Use graph paper to visualise and measure areas of irregular shapes.

• Compare area and perimeter to understand their differences.

• Memorise the formulas for calculating the area and perimeter of common shapes.

• Practice converting different units of measurement (like cm to m) when calculating area.

Conclusion

Vedantu’s Maths Area and its boundary Class 5 Notes provide students with an easy-to-understand approach to learning important concepts like area and perimeter. The notes simplify the process of calculating the area of regular and irregular shapes, while also explaining how to measure boundaries using clear formulas. By practising through these notes, students can strengthen their understanding of geometry and build a solid foundation for future topics. By using these notes, students prepare confidently for their exams. Use these notes to review key points and practice problem-solving with ease.

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