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XYZ is a circle enter o and a radius 7cm Find t... - JAMB Mathematics 2003 Question

XYZ is a circle enter o and a radius 7cm. Find the area of the shaded region. θ = 45 x 2 = 90
A
84cm2
B
77cm2
C
38cm2
D
14cm2
correct option: d

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

= 77/2cm2

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

Area of shaded region = 77/2 - 49/2

11
2

= 28/2

= 14cm2

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