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

In 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
$$\begin{gathered} =\frac{1}{4}\mathrm{\pi }{\left(\mathrm{OB}\right)}^2-{\left(\mathrm{OA}\right)}^2 \\ =\frac{1}{4}\times \frac{22}{7}\times 882-441 \\ =693-441 \\ =252{\mathrm{cm}}^2 \end{gathered}$$
14π(OB)2−(OA)2=14×3.14×800−400=628−400=228 cm2
Hence, the area of the shaded region is 252 cm².