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Question
In the following figure a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 21 cm, find the area of the shaded region.
Solution
Construction: Join OB
n right triangle AOB
OB2 = OA2 + AB2
= 212 + 212
= 441 + 441
= 882
∴ OB2 = 882
Area of the shaded region = Area of quadrant OPBQ − Area of Square OABC
\[= \frac{1}{4}\pi \left( OB \right)^2 - \left( OA \right)^2 \]
\[ = \frac{1}{4} \times \frac{22}{7} \times 882 - 441\]
\[ = 693 - 441\]
\[ = 252 {cm}^2\]
Hence, the area of the shaded region is 252 cm2.
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