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Question
In the given figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region. [Use Π = 22/7]
Solution
As ABC is a quadrant of the circle, ∠BAC will be of measure 90º.
In ΔABC,
BC2 = AC2 + AB2
= (14)2 + (14)2
BC = 14sqrt2
Radius (r1) of semi-circle drawn on BC = `(14sqrt2)/2 = 7sqrt2 cm`
Area of ΔABC = 1/2 x AB x AC
= 1/2 x 14 x 14
= 98 cm2
Area of sector ABDC = `90^@/360^@ xx pir^2`
`= 1/4 xx 22/7 xx 14 xx 14`
=154 cm2
Area of semi circle drawn of BC = `1/2xxpixxr_1^2 = 1/2 xx 22/7 xx (7sqrt2)^2`
`= 1/2 xx 22/7xx 98 = 154 cm^2`
Area of shaded region = Area of semi- circle - (Area of sector ABDC - Area of ΔABC) = 154 - (154-98)
= 98 cm2
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