Question

ABCD is a rectangle with AB = 14 cm and BC = 7 cm. Taking DC, BC and AD as diameters, three semi-circles are drawn as shown in the figure. Find the area of the shaded region.

Answer 1

Given:
Length of a rectangle (AB) = DC = 14 cm
Breadth of a rectangle( BC) = AD =7 cm $\frac{1}{2}$ $\pi$ ${\frac{14}{2}}^2$

Area of semicircle with diameter DC = $\frac{1}{2}$ $\pi$ ${\frac{14}{2}}^2$ = $\frac{1}{2}$ $\times$ $\frac{22}{7}$ $\times$ ${\frac{14}{2}}^2$
= 11 $\times$ 7 = 77 cm²

Area of rectangle (ABCD) = Length × Breadth = AB × DC = 14 $\times$ 7 = 98 cm²

Area of 2 semi circle with diameter BC & AD= 2 $\times$ $\frac{1}{2}$ $\times$ $\pi$ $r^2$ =2× 1/2πr² =(22/7) × (7/2)² = 11 ×7 / 2 = 77 /2 cm²

Area of shaded region = Area of rectangle ABCD - area of semicircle with diameter DC + Area of 2 semicircle with diameter BC and AD

Area of shaded region = 98 - 77 + 77/2
= 21 + 77/2 = (42 +77)/2 = 119/2 = 59.5 cm²
Area of shaded region = 59.5 cm²

Hence, the Area of shaded region is 59.5 cm².

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