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In the given figure, ABC is a quadrant of a circle of radius 14 $cm$ and a semicircle is drawn with BC as diameter. What is the area of the shaded region?

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98 cm 2

88 cm 2

90 cm 2

108 cm 2

answer is A.

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Detailed Solution

Given that the radius of a circle is 14

cm

and BC is the diameter of a semi-circle.
Question Image

We have the following formulae,
Area of semi-circle

= π r 2 2

Area of quadrant

= π r 2 4

Area of triangle

= 12 × b × h

We have,
AB = AC = 14cm

∴ B C = 142 = 2 × radius radius = 1422 r = 72 c m

Area of the semi-circle will be,

= 12 × 227 × 72 × 72 = 154 cm 2

Area of the quadrant will be,

= 14 × 227 × 14 × 14 = 154 cm 2

Area of the triangle ABC will be,

12 × 14 × 14 = 98 cm 2

Thus the area of the shaded region is,
Area of the semicircle-(Area of the quadrant- area of the triangle)

= 154 − (154 − 98) = 154 − 56 = 98 c m 2

Thus, the area of the shaded region is

98 cm 2

.
Therefore the correct option is 1.

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