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 )

---

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
]

---

Step 2: 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
]

---

Step 3: Area of segment

[
A = 60\pi - 36
]

---

Step 4: Approximate value ((\pi \approx 3.14))

[
60\pi \approx 188.4
]

[
A \approx 188.4 - 36 = 152.4
]

---

✅ Final Answer:

[
\boxed{60\pi - 36 \approx 152.4\ \text{cm}^2}
]