XYZ is a circle with center O and a radius 7cm. Find the area of the shaded region.
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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\(^2\)
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\(^2\)