Question

In the given figure a square OABC is inscribed in a quadrant OPBQ. If OA =20cm, find the area of the shaded region.

Answer 1

Answer:

880/7 or 40π

Step-by-step explanation:

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Answer 2

Radius of quadrant OPBQ is

$\sf{OB=\sqrt{ {OA}^{2} + {AB}^{2} } }$

= $\sf{ \sqrt{ {20}^{2} + {20}^{2} } cm}$

= $\sf{20 \sqrt{2} cm}$

Area of quadrant OPBQ

= $\sf{\frac{1}{4} \times 3.14 \times {(20 \sqrt{2} )}^{2}}$

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

= $\sf{{628cm}^{2}}$

Area of square OABC = $\sf{ {(20cm)}^{2}}$

= $\sf{{400cm}^{2}}$

Hence, the area of the shaded region

= $\sf{(628 - 400) {cm}^{2}}$

= ${\boxed{\sf{{228cm}^{2}}}}$