Question

In the following figure a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 21 cm, find the area of the shaded region.

 

Answer 1

Construction: Join OB

n right triangle AOB
OB² = OA² + AB²
= 21² + 21²
= 441 + 441
= 882
∴ OB² = 882
Area of the shaded region = Area of quadrant OPBQ − Area of Square OABC

\[= \frac{1}{4}\pi \left( OB \right)^2 - \left( OA \right)^2 \]
\[ = \frac{1}{4} \times \frac{22}{7} \times 882 - 441\]
\[ = 693 - 441\]
\[ = 252 {cm}^2\]

Hence, the area of the shaded region is 252 cm².