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 $\pi$ = 3.14.]

Answer 1

S

In ΔOAB,

\({OB} ^{2} = {OA}^{2} + {AB}^{2}

= {20}^{2} + {20}^{2} \)

OB = $20\sqrt{2}$

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

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

$\frac{1}{4}\times 3.14\times 800=628{cm}^2$

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

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

$=(628-400)c{m}^2\to 228c{m}^2$