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Question

# In Fig. 13.113, ABCD is a square with side $2\sqrt{2}$ cm and inscribed in a circle. Find the area of the shaded region. (Use π = 3.14)

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Solution

## ABCD is a square. Side of the square = AB = $2\sqrt{2}\mathrm{cm}$ We know Length of the diagonal of square = $\sqrt{2}$ × Side of the square ∴ BD = Diameter of the circle = Length of the diagonal of square = $\sqrt{2}×2\sqrt{2}$ = 4 cm ⇒ Radius of the circle = $\frac{\mathrm{BD}}{2}$ = 2 cm Now, Area of shaded region = Area of the circle − Area of the square ABCD $=\mathrm{\pi }{\left(\frac{\mathrm{BD}}{2}\right)}^{2}-{\left(\mathrm{AB}\right)}^{2}\phantom{\rule{0ex}{0ex}}=3.14×{\left(2\right)}^{2}-{\left(2\sqrt{2}\right)}^{2}\phantom{\rule{0ex}{0ex}}=3.14×4-8$ $=12.56-8\phantom{\rule{0ex}{0ex}}=4.56{\mathrm{cm}}^{2}$ Thus, the area of the shaded region is 4.56 cm2.

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