Chapter 12.5, Problem 49SR

To determine

To find the area of each shaded region.

Answer to Problem 49SR

  $30$ square centimeters

Explanation of Solution

Given:

  $$

Rectangle:

Length $=10$ centimeters

Breadth $=5$ centimeters

Formula used :

Area of a rectangle $=length\times breadth$

Area of a circle $=\pi r^2$ , where $r$ is the radius of the circle.

Calculation:

  

From the figure,

  $BC=$ diameter of the circle$\Rightarrow d=5$

  $\Rightarrow r=\frac{d}{2}$

  $\Rightarrow r=2.5$ centimeters

Now for the area of circle,

  $\Rightarrow \pi r^2$

Putting the value of $r=2.5$

  $\Rightarrow 3.14\times 2.5\times 2.5$

  $\Rightarrow 19.6$ square centimeters

So, area of the circle $=19.625$ square centimeters.

Now for the area of rectangle $ABCD$ ,

Length $=10$ centimeters

Breadth $=5$ centimeters

And, area $=$ length $\times$ breadth

  $\Rightarrow 10\times 5$

  $\Rightarrow 50$ square centimeters

So, area of the rectangle $ABCD$

  $=50$ square centimeters.

Now,

Hence, area of the shaded region $=$ Area of the rectangle $ABCD$

  $-$ Area of the circle

  $\Rightarrow 50-19.6$

  $\Rightarrow 30.4$

Hence, area of the shaded region $\approx 30$ square centimeters.

Conclusion:

Therefore, the area of the shaded region in the given figure is $30$ square centimeters.