Question

In the following figure, ABCD is a square with side `2sqrt(2)` cm and inscribed in a circle. Find the area of the shaded region. (Use π = 3.14).

Answer 1

Given: ABCD is a square with side = `2sqrt(2)` cm, inscribed in a circle.

Step-wise calculation:

1. Diagonal of square = side × `sqrt(2)`

= `(2sqrt(2)) xx sqrt(2)` 

= 4 cm

⇒ Diameter of circle = diagonal = 4 cm

So radius r = 2 cm.

2. Area of circle = πr²

= π × 2²

= 4π cm² 

Using π = 3.14

⇒ Area(circle) = 4 × 3.14

= 12.56 cm²

3. Area of square = `(2sqrt(2))^2`

= 4 × 2

= 8 cm²

4. Shaded area = Area(circle) – Area(square)

= 4π – 8

Numeric value = 12.56 – 8

= 4.56 cm²

Area of the shaded region = 4π – 8 cm²

= 4.56 cm²    ...(Using π = 3.14)