Question

In figure find the area of the shaded region [Use π = 3.14]

Answer 1

Answer:

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Answer 2

Area of the shaded region is 154.87 cm².

Solution:

The image given in the question is attached below.

First: Find the radius of the semicircle:

$\bold{Radius \ of \ 4 \ semicircle = r = \frac{14-6}{4}=\frac{8}{4}=2 \ cm}$

Second: Find the sides of the square inside big square:

$\bold{Side \ of \ square = s = 2r = 2\times 2=4}$

Third: Find the area of small square:

$\bold{Area \ of \ small \ sqaure = a = s^2 = 4^2 = 16 \ cm^2}$

Fourth: Find the area of four semicircle:

$\bold{Area \ of \ four \ semicircle= sm = 4\times \frac{\pi r^2}{2}=2(\pi)4=8\pi \ cm^2}$

Fifth: Find the area of bigger square:

$\bold{Area \ of \ bigger \ square = S^2 = 14 \times 14 = 196 \ cm^2}$

S = Side of the square given in the diagram

Sixth: Find the area of shaded region:

Area of shaded region = Area of bigger square - Area of small square - Area of four semicircle

$\bold{Area \ of \ shaded \ region= S^2 - s^2 - sm}$

$\bold{Area \ of \ shaded \ region=196-16-8\pi}$

$\bold{Area \ of \ shaded \ region=180-25.13}$

$\bold{Area \ of \ shaded \ region=154.87 \ cm^2}$