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Find the area of the shaded region given in figure.
$Find the area of the shaded region given in figure.\n \n \n ...$

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148 c m^{2}

152 c m^{2}

150 c m^{2}

154.88 c m^{2}

answer is A.

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Detailed Solution

Given that, a square consisting of 4 semicircles and a small square at its centre.
$Find the area of the shaded region given in figure.\n \n \n ...$ There are four semicircles that mean it has two complete circles.
Let the side of small square be

2 x

.
So, clearly the radius of each semicircle is

= x

According to the figure,
Radius of Semicircle

\times 2 +

One side of Small Square

+ 2 \times 3 = 14

\Rightarrow 2 x + 2 x + 2 \times 3 = 14

\Rightarrow

4x + 6 = 14

\Rightarrow

4x = 8

\Rightarrow

x = 2
Calculating the area of the small square that is at the centre with side

= 2 x

. Area

= {(side)}^{2}

\Rightarrow (2 x)^{2}

\Rightarrow {(2 \times 2)}^{2}

\Rightarrow {(4)}^{2}

\Rightarrow

16
Calculating the area of two circles,
Area

= 2 × π r 2

⇒ 2 × 227 × 22

\Rightarrow

25.12

{cm}^{2}

Calculating the area of non-shaded region subtract the sum of 2 circles and small square from the area of the bigger square.

142 − 25.12 + 16 ⇒ 196 − 4112

⇒ 154.88

Thus, the area of the shaded region is

154.88 c m 2

.
Hence the correct option is 1.

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