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XYZ is a circle enter o and a radius 7cm. Find the area of the shaded region. θ...


Question

XYZ is a circle enter o and a radius 7cm. Find the area of the shaded region. θ = 45 x 2 = 90

Options

A) 84cm2

B) 77cm2

C) 38cm2

D) 14cm2

The correct answer is 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
= 77/2cm2
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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Dicussion (1)

  • 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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