Question
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The area of an equilateral ΔABC is 17320.5 cm2. A circle is drawn taking the vertex of the triangle as centre. The radius of the circle is half the length of the side of triangle. Find the area of the shaded region (in cm2) . (π = 3.14 , √3 =1.73205)
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Answer: Option A
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Area of shaded region = area of ΔABC - 3 (Area of sector BPR)
Let 'a' be the side of the equilateral ΔABC.
Using area of an equilateral triangle = √34a2,
√34a2 = 17320.5
Solving, a2=17320.5×4√3
⟹a2=17320.5×41.73205
⟹a2=17320.5×417320.5×10−4
⟹a=2×102
⟹ a = 200 cm.
Radius of the circles = 12×200 = 100 cm
Now, using area of a sector when the degree measure of the angle at the centre is θ = θ360πr2
∴ Required area =17320.5 - 3[60360×3.14×1002 ]
∴ Required area = 1620.5cm2
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