In the given figure, ABCD is a square of side 4 cm.
Question:

In the given figure, ABCD is a square of side 4 cm. A quadrant of a circle of radius 1 cm is drawn at each vertex of the square and a circle of diameter 2 cm is also drawn. Find the area of the shaded region.

[Use $\pi=3.14 .$ ]

 

Solution:

Area of the square $A B C D=(\text { Side })^{2}$

$=4^{2}$

$=16 \mathrm{~cm}^{2}$

Area of the circle $=\pi r^{2}$

Radius = 1 cm

Area $=3.14 \times(1)^{2}$

$=3.14 \mathrm{~cm}^{2}$

Area of the quadrant of one circle $=\frac{1}{4} \pi r^{2}$

$=\frac{1}{4} \times 3.14 \times 1^{2}$

 

$=0.785 \mathrm{~cm}^{2}$

Area of the quadrants of four circles $=0.785 \times 4=3.14 \mathrm{~cm}^{2}$

Area of the shaded region = Area of the square Area of the circle  Area of the quadrants of four circles

$=16-3.14-3.14=9.72 \mathrm{~cm}^{2}$

 

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