Question

What is the area of the segment formed by a chord in a circle of radius 12 cm, if the angle subtended at the center is 150°?

• A. 60п-36
• B. 36П-36
• C. 60-72
• D. 36-72

Answer 1

Answer:

A. 60п-36

Area of a segment = Area of sector − Area of triangle.

Given:

• Radius (r = 12) cm

• Angle ( \theta = 150^\circ )

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Step 1: Area of sector

$A_{\text{sector}} = \frac{\theta}{360^\circ} \pi r^2$

$= \frac{150}{360} \times \pi \times 144$
$= \frac{5}{12} \times 144\pi$
$= 60\pi$

Area of triangle

$A_{\triangle} = \frac{1}{2} r^2 \sin\theta$

$= \frac{1}{2} \times 144 \times \sin150^\circ$

Since $(\sin150^\circ = \frac{1}{2}):$

$= 72 \times \frac{1}{2} = 36$

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Step 3: Area of segment

$A = 60\pi - 36$