2003
Mathematics
67ca00ce0c643c71d77dee1f
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.
B 77cm2
C.
38cm2
D.
14cm2
Correct Answer: 14cm2
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 1 1 2 = 28/2 = 14cm2
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 1 1 2 = 28/2 = 14cm2THIS WEEK's
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