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. $\angle$EFG = $\angle$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
• B. False

Answer 1

The correct option is B False

Area of shaded region in figure 1 = Area of rhombus - Area of circle
$\frac{1}{2}\times 6\times 8-\pi \times {2.4}^2=24-5.76\pi$
Area of shaded region in figure 2 = Area of parallelogram - Area of two sectors with angle 120 degrees and radius 2.4 cm.
$=6\times 4-2\times \left(\frac{120}{360}\right)\times \pi \times {2.4}^2=24-3.84\pi$
Hence, area of shaded region in figures 1 and 2 are not equal.