In the below figure, find the area of the shaded region. (Use $ \pi=3.14) ."

To do: 

We have to find the area of the shaded region.

Solution:

Side of the larger square $= 14\ cm$

From the figure,

$14=3+3+r+2r+r$

$4r=14-6$

$r=\frac{8}{4}$

$r=2\ cm$

This implies,

Radius of each semi-circle $= 2\ cm$

Side of the inner square $= 4\ cm$

Area of the inner square $=  4 \times 4$

$=16\ cm^2$

Therefore,

Area of four semicircles $= 4 \times \frac{1}{2} \pi r^2$

$= 2 \times 3.14 \times 2^2$

$= 8 \times 3.14$

$= 25.12\ cm^2$

Area of the shaded region $=$ Area of the large square $-$ Area of central part

$= (14)^2-(16+ 25.12)\ cm^2$

$= 196-41.12\ cm^2$

$= 154.88\ cm^2$

The area of the shaded region is $154.88\ cm^2$.

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Updated on: 10-Oct-2022

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