**Chapter 12 Perimeter and Area Set 12.2**

Question 1.

If the side of a square is 12 cm, find its area.

Solution:

Area of a square = (side)² = (12)²

= 144 sq. cm.

∴ The area of the square is 144 sq. cm.

Question 2.

If the length of a rectangle is 15 cm and breadth is 5 cm, find its area.

Solution:

Area of a rectangle = length × breadth

= 15 × 5

= 75 sq. cm.

∴ The area of the rectangle is 75 sq. cm.

Question 3.

The area of a rectangle is 102 sq. cm. If its length is 17 cm, what is its perimeter?

Solution:

Area of a rectangle = length × breadth

∴ 102 = 17 × breadth

∴ breadth = 102/17 = 6 cm

Perimeter of rectangle = 2 (length + breadth)

= 2 (17 + 6)

= 2 × 23

= 46 cm

∴ The perimeter of rectangle is 46 cm.

Question 4.

If the side of a square is tripled, how many times will its area be as compared to the area of the original square?

Solution:

Let the side of the square be a.

∴ Area of a square = (side)² = a²

New side of the square = 3 × a = 3a

∴ New area of the square = (3a)²

= 9a²

= 9 × area of original square

∴ If the side of a square is tripled, its area will become 9 times the area of the original square.

**Intext Questions and Activities**

Question 1.

A rectangular playground is 65m long and 30m wide. A pathway of 1.5 m width goes all around the ground, outside it. Find the area of the pathway. (Textbook pg. no. 82)

Solution:

The playground is rectangular.

₹ABCD is the playground. Around it is a pathway 1.5 m wide.

Around ₹ABCD we get the rectangle ₹PQRS

Length of new rectangle PQRS = 65 + 1.5 + 1.5 = 68 m

Breadth of new rectangle PQRS = 30 + 1.5 + 1.5 = 33m

Area of path = Area of rectangle PQRS – Area of rectangle ABCD = 68 x 33 – 65 x 30

= 2244 – 1950

= 294 sq m

Question 2.

Is there another way to find the area of the pathway in the problem above? (Textbook pg. no. 82)

Solution:

Yes. The area of the pathway can be found by dividing it into rectangles and adding the areas of these rectangles.

Length of rectangle 1 = 30 + 1.5 + 1.5 = 33 m

Breadth of rectangle 1 = 1.5 m

∴ Area of rectangle 1 = 33 x 1.5

= 49.5 sq. m

Area of rectangle 4 = Area of rectangle 1

= 49.5 sq. m.

Length of rectangle 2 = 65 m

breadth of rectangle 2 = 1.5 m

∴ Area of rectangle 2 = 65 x 1.5

= 97.5 sq. m.

Area of rectangle 3 = area of rectangle 2

= 97.5 sq. m.

∴ Area of pathway = Sum of area of the 4 rectangles = 49.5 + 49.5 + 97.5 + 97.5

= 294 sq. m.

Question 3.

The length and the width of a mobile phone are 13 cm and 7 cm respectively. It has a screen PQRS as shown in the figure. What is the area of the screen? (Textbook pg. no. 82)

Solution:

ABCD is the rectangle formed by the edges of the mobile. PQRS is the rectangle formed by leaving a 1.5 cm wide edge alongside AB, BC, and DC, and a 2 cm edge alongside DA.

Length of rectangle PQRS = 9.5 cm

Breadth of rectangle PQRS = 4 cm

Area of screen = Area of rectangle PQRS = 9.5 x 4

= 38 sq .cm