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Question

In the first figure, ABCD is a rhombus with diagonals of length 6 cm and 8 cm respectively. The circle inscribed in the rhombus is of radius 2.4cm. The second figure shows a parallelogram EFGH with EF = GH = 6 cm and the perpendicular distance between EF and GH is 4 cm. EFG = EHG = 120 degrees. Two arcs are drawn with centres as F and H, with radii 2.4 cm. The area of shaded region in figures 1 and 2 are equal. State true or false.

A
True
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B
False
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Solution

The correct option is B False
Area of shaded region in figure 1 = Area of rhombus - Area of circle
12×6×8π×2.42=245.76π
Area of shaded region in figure 2 = Area of parallelogram - Area of two sectors with angle 120 degrees and radius 2.4 cm.
=6×42×(120360)×π×2.42=243.84π
Hence, area of shaded region in figures 1 and 2 are not equal.

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