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Question
In the equilateral Δ ABC of side 14 cm, side BC is the diameter of a semicircle as shown in the figure below. Find the area of the shaded region. (Take π = 22/7 and √3 = 1.732)
Solution
Area of shaded part = Area of equilateral Δ ABC + Area of semicircle
= `sqrt3/4 a^2 + 1/2` πr2
Given a = 14 cm and r = `14/2` = 7 cm
∴ Area of shaded part = `sqrt3/4 xx 14^2 + 1/2 xx 22/7 xx 7 xx 7`
= `(1.732 xx 14 xx 14)/4 + 11 xx 7`
= 1.732 x 7 x 7 + 77
= 84.868 + 77
= 161.868 sq.cm.
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