# In the Given Figure, If a is the Centre of the Circle. ∠ Par = 30°, Ap = 7.5, Find the Area of the Segment Pqr ( π = 3.14) - Geometry

#### Question

In the given figure, if A is the centre of the circle. $\angle$ PAR = 30°, AP = 7.5, find the area of the segment PQR ( $\pi$  = 3.14)

#### Solution

Radius of the circle, r = 7.5 cm
∠​PAR = θ = 30º
∴ Area of segment PQR

$= r^2 \left( \frac{\pi\theta}{360°} - \frac{\sin\theta}{2} \right)$
$= \left( 7 . 5 \right)^2 \left( \frac{3 . 14 \times 30° }{360° } - \frac{\sin30° }{2} \right)$
$= 56 . 25 \times \left( \frac{3 . 14}{12} - \frac{1}{4} \right)$
$= 56 . 25 \times 0 . 01167$
$= 0 . 65625 {cm}^2$

Thus, the area of the segment PQR is 0.65625 cm2.

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