Find the area of the shaded region in Fig. 8, if $PQ = 24$ cm, $PR = 7$ cm and $O$ is the centre of the circle.

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Question

Find the area of the shaded region in Fig. 8, if $PQ = 24$ cm, $PR = 7$ cm and $O$ is the centre of the circle.

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Accepted Answer

Step 1: $\angle P = 90°$ (angle in semicircle). $QR = \sqrt{24^2 + 7^2} = 25$ cm. Radius $= \frac{25}{2}$ cm
Step 2: Area of shaded portion $=$ Area of semi circle $-$ Area of $	riangle PQR$
Step 3: $= \frac{1}{2} 	imes \frac{22}{7} 	imes \left(\frac{25}{2}ight)^2 - \frac{1}{2} 	imes 7 	imes 24$
Step 4: $= 161.54$ cm$^2$

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