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Question : A right-angled isosceles triangle is inscribed in a semi-circle of radius 7 cm. The area enclosed by the semi-circle but exterior to the triangle is:

Option 1: 14 cm2

Option 2: 28 cm2

Option 3: 44 cm2

Option 4: 68 cm2


Team Careers360 23rd Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

Correct Answer: 28 cm 2


Solution :
Area of the semi-circle
= $\frac{1}{2} \pi r^2$
= $\frac{1}{2}\times  \frac{22}{7}\times  7^2$
= 77 cm 2
The altitude of the isosceles triangle OC is $r$ = 7 cm.
The base of the isosceles triangle AB is the diameter = $2 r$ = 14 cm.
Area of the Isosceles triangle ABC
= $\frac{1}{2}$ × Base × Height
= $\frac{1}{2}\times 14\times 7$
= 49 cm 2
So, the area enclosed by the semi-circle but exterior to the triangle = 77 - 49 = 28 cm 2
Hence, the correct answer is 28 cm 2 .

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