Question

A rectangular playground has two semi-circles added to its outside with its smaller sides as diameters. If the sides of the rectangle are 120 m and 21 m, find the area of the playground `(π = 22/7)`.

Answer 1

Given: A rectangle of sides 120 m and 21 m with two semicircles attached on the 21 m sides. So, the two semicircles together form a full circle of diameter 21 m. `π = 22/7`.

Step-wise calculation:

1. Area of rectangle

= Length × Width 

= 120 × 21

= 2520 m²

2. Diameter of circle formed by the two semicircles = 21 m

Radius r = `21/2` 

= 10.5 m

3. Area of that circle

= πr²

= `22/7 xx (10.5)^2`

(10.5)² = 110.25

`22/7 xx 110.25 = 22 xx 15.75`

= 346.5 m²

4. Total area

= Area of rectangle + Area of circle 

= 2520 + 346.5

= 2866.5 m²

The area of the playground is 2866.5 m².