In a circle of radius 14 cm, a chord makes a right angle at the centre. What is the area of the smaller segment cut off by the chord? Take $\pi = \frac{22}{7}$ .

56 cm²Correct answerYour answer98 cm²Correct answerYour answer154 cm²Correct answerYour answer252 cm²Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Quarter sector area = $\frac{1}{4} \times \frac{22}{7} \times 14 \times 14 = 154$ cm².
The triangle formed by the chord and the two radii has area $\frac{1}{2} \times 14 \times 14 = 98$ cm².
Segment = sector − triangle = $154 - 98 = 56$ cm².

Worth noting

154 cm² is the whole sector and 98 cm² is only the triangle. The segment is the difference, not the sum (252 cm²).

Ten questions from Mensuration: Areas and Volumes, at your own pace.

In a circle of radius 14 cm, a chord makes a right angle at the centre. What is the area of the smaller segment cut off by the chord? Take π=227\pi = \frac{22}{7}π=722​.