Question

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Find the area of the shaded figure

step by step explanation needed ​

Answer 1

Answer:

Area of the shaded region is 42 cm^2.

Step-by-step explanation:

As we can see that all the sides of this quadrilateral are equal. So it is obvious that the given quadrilateral is a square. And, there are two semi circles whose diameter is the side of the square.

From the properties of square,

Area of square = side^2

Thus the area of this square should be ( 14 cm )^2, that is 196 cm^2

= > Radius of the circle = Diameter / 2

= > Radius of the circle = side of square / 2

= > Radius of circle = 14 cm / 2

= > Radius of circle = 7 cm

And, from the properties of circle, we know :

Area of semi - circle = 1 / 2 πr^2

So, as the radius of both the semi circles is same,

= > Area of two semi - circles = 2 x 1 / 2 x 22 / 7 x ( 7 cm )^2

= > Area of two semi - circles = 22 / 7 x 7 x 7 cm^2

= > Area of two semi  - circles = 154 cm^2

On observing the diagram we can say that the area of the shaded region will be there is we subtract / remove the area of two semicircles from the area of the square.

Therefore,

Area of the shaded region = 196 cm^2 - 154 cm^2

Area of the shaded region = 42 cm^2

Answer 2

$\textbf{\large{\underline{Answer :-}}}$

The area of the shaded figure is 42 sq.cm

$\textbf{\large{\underline{Explaination:-}}}$

Area of the shaded portion =

$\texttt{Area of the square ABCD - Area of 2 semicircles}$

Thus, the Length of the diameter of the circle = 14 cm

The Radius =

$\tt{ \Rightarrow \dfrac{14}{2} }$

$\therefore$The Radius is 7 cm

Also, area of two semicircles = Area of one circle

As we know, Area of Circle =

$\tt{ \Rightarrow \pi \: r^{2} }$

$\tt{ \Rightarrow \dfrac{22}{7} \times 7 \times 7}$

$\tt{ \Rightarrow \frac{22}{{ \cancel{7}}} \times 7 \times { \cancel{7}}}$

$\tt{ \Rightarrow22 \times 7 }$

$\tt{ \Rightarrow154 }$

$\tt{ \Rightarrow 154 \:cm ^{2} }$

Area of Square =

$\tt{ \Rightarrow (side)^{2} }$

$\tt{ \Rightarrow (14)^{2} }$

$\tt{ \Rightarrow 196}$

$\tt{ \Rightarrow 196 \: cm^{2} }$

As the area of shaded portion =

$\texttt{Area of the square ABCD - Area of 2 semicircles}$

$\tt{ \Rightarrow 196 - 154}$

$\tt{ \Rightarrow 42}$

$\tt{ \Rightarrow 42 \: cm ^{2} }$

$\therefore$The area of the shaded portion is 42 cm²