In figure, a square OABC is inscribed in a quadrant OPBQ . If OA = 20 cm, find the area of the shaded region. (Use \( \pi \ = \ 3.14 \))

Radius of the quadrant \( = \ OB = \sqrt{OA^2 \ + \ AB^2} \ \)
\( = \sqrt{20^2 \ + \ 20^2} \ \)
\( = \ 20 \sqrt{2} \) cm

\(\therefore \) Area of quadrant OPBQ

\(= \ \frac{1}{4} \ \pi r^2 \ \)
\( = \ \frac{1}{4} \ × \ 3.14 \ × \ (20 \sqrt{2})^2 \ \)
\( = \frac{1}{4} \ × \ 3.14 \ × \ 800 \ \)
\( = \ 628 \) cm²

Area of the square OABC

\(= \ (20)^2 \ = \ 400 \) cm²

So, area of the shaded region

= Area of quadrant - Area of square OABC

\( = \ 628 \ - \ 400 \ = \ 228 \) cm²