Question

In Fig. OC = 20 cm. In sector OQBP, square OABC is inscribed. Find the area of the shaded region.

Answer 1

In ΔOAB,

$O{B}^2=O{A}^2+A{B}^2$

= $(20{)}^2+(20{)}^2$

OB = $20\sqrt{2}$

Radius (r) of circle = $20\sqrt{2}$ cm

Area of quadrant OPBQ = $\frac{{90}^{\circ }}{{360}^{\circ }}$ $\times$ 3.14 $\times$ ($20\sqrt{2}{)}^2$

= $\frac{1}{4}$ $\times$ 3.14 $\times$800

= 628 $c{m}^2$

Area of OABC = $(Side{)}^2$ = $(20{)}^2$ = 400 $c{m}^2$

Area of shaded region = Area of quadrant OPBQ − Area of OABC

= (628 − 400) $c{m}^2$

= 228 $c{m}^2$