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Find the area of the shaded region in Fig. 4, if $ABCD$ is a rectangle with sides $8\ cm$ and $6\ cm$ and $O$ is the center of circle. $( Take\ \pi= 3.14)$
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Given: Sides of the rectangle $=8\ cm$ and $6\ cm$. $O$ is the center of circle.

To do: To find the area of the shaded region.

Solution:

Here, diagonal $AC=$diameter of the circle.

$\vartriangle ABC$, is a right triangle.

Using Pythagoras theorem

$\Rightarrow AC^{2}=AB^{2}+BC^{2}$

$\Rightarrow AC^{2}=8^{2}+6^{2}$

$\Rightarrow AC^{2}=64+36=100$

$\Rightarrow AC=\sqrt{100}=10\ cm$

Radius of the circle, $OC= \frac{diameter(AC)}{2}$

                                        $ =\frac{10}{2}$

                                         $ =5\ cm$

Area of the circle $=\pi r^{2}=3.14\times (5)^{2}=78.5\ cm^{2}$

Area of the rectangle $=8\times6=48\ cm^{2} $

Area of the shaded region $=$Area of the circle$-$Area of rectangle

                                            $=78.5-48$

                                            $=30.5\ cm^{2}$

Therefore, The area of shaded region is $30.5\ cm^{2}$.

 

Updated on: 10-Oct-2022

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