In the figure, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region.
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Given:

ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touch externally two of the remaining three circles.

To do: 

We have to find the area of the shaded region.

Solution:

Length of the side of the square $ABCD= 14\ cm$

This implies,

Radius of each of the circle $r= 7\ cm$

Therefore,

Area of the shaded region $=$ Area of the square $-$ Area of four quadrants inside the square

$=(14)^{2}-4 \times \frac{1}{4} \pi 7^{2}$

$=(14)^{2}-\frac{22}{7} \times 7^2$

$=196-154$

$=42 \mathrm{~cm}^{2}$

The area of the shaded region is $42\ cm^2$.

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Updated on: 10-Oct-2022

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