NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 6: Mensuration - Fill in the Blanks

Question 12

Step 1: Understand the given shapes

We have a rectangle with sides 6 cm and 2 cm, and a square. They both have the same perimeter.

Step 2: Perimeter of the rectangle

Perimeter of a rectangle = ( 2 imes ( ext{length} + ext{breadth}) )

Here, length = ( 6 ext{ cm} ) and breadth = ( 2 ext{ cm} ).

So, ( ext{Perimeter} = 2 imes (6 + 2) )

( = 2 imes 8 )

( = 16 ext{ cm} )

Step 3: Area of the rectangle

Area of a rectangle = ( ext{length} imes ext{breadth} )

( = 6 imes 2 )

( = 12 ext{ cm}^2 )

Step 4: Use the same perimeter for the square

The square has the same perimeter as the rectangle.

So, square’s perimeter = ( 16 ext{ cm} )

Step 5: Find the side of the square

Perimeter of a square = ( 4 imes ext{side} )

So, ( 4 imes ext{side} = 16 )

( ext{side} = dfrac{16}{4} )

( = 4 ext{ cm} )

Step 6: Area of the square

Area of a square = ( ext{side}^2 )

( = 4^2 )

( = 16 ext{ cm}^2 )

Final answers

(a) Area of the rectangle = 12 cm²

(b) Area of the square = 16 cm²