XYZ is a circle with center O and a radius 7cm. Find the area of the shaded region.
-
A.
84cm2 -
B.
77cm2 -
C.
38cm2 -
D.
14cm2
Correct Answer: Option D
Explanation
θ = 45 x 2 (∠ at center twice ∠ at θ)
θ = 90°
Area of sector = θ/360 x πr2
= 90/360 x 22/7 x 7 x 7
= 77/2cm(^2)
Area of triangle = 1/2 ab sin θ
= 1/2 x 7 x 7 sin 90
= 1/2 x 7 x 7 x 1
= 49/2 cm(^{2})
Area of shaded region = 77/2 – 49/2
= 28/2
= 14cm(^2)