Question

In the following, a square OABC is inscribed in a quadrant OPBQ. If OA = 15 cm, find the area of shaded region (use π = 3.14).

Answer 1

Given:

Square OABC is inscribed in quadrant OPBQ.

OA = side of square = 15 cm.

Take π = 3.14.

Step-wise calculation:

1. Radius of the quadrant = OB

= Diagonal of the square

= `OAsqrt(2)` 

= `15sqrt(2)` cm

⇒ `r^2 = (15sqrt(2))^2`

= 15² × 2 

= 450

2. Area of the quadrant = `(1/4)·π·r^2`

= `(1/4)·π·450`

= 112.5·π cm²

Substitute π = 3.14:

112.5 × 3.14 

= 353.25 cm²

3. Area of the square = side²

= 15²

= 225 cm²

4. Shaded area = (Area of quadrant) – (Area of square)

= 353.25 – 225

= 128.25 cm² 

Area of the shaded region = 128.25 cm².