Question

In the given figure, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 20 cm, find the area of the shaded region. [Use π = 3.14.] [CBSE 2014]

Answer 1

Construction: Join OB

In right triangle AOB
OB² = OA² + AB²
= 20² + 20²
= 400 + 400
= 800
∴ OB² = 800
Area of the shaded region = Area of quadrant OPBQ − Area of Square OABC
$$\begin{gathered} =\frac{1}{4}\mathrm{\pi }{\left(\mathrm{OB}\right)}^2-{\left(\mathrm{OA}\right)}^2 \\ =\frac{1}{4}\times 3.14\times 800-400 \\ =628-400 \\ =228{\mathrm{cm}}^2 \end{gathered}$$
Hence, the area of the shaded region is 228 cm².