Question

In the given figure, $ABCD$ is a rectangle and three circles are positioned as shown. Find the area of the shaded region, rounded to the nearest ${cm}^2$.

Answer 1

Let the diameter of one circle be $d.$

Then,

$3d=24cm$

$d=8cm$

So, radius of each circle will be $4cm.$

The breadth of the rectangle will be equal to the diameter of the circle $8cm.$

Let the area of the shaded portion be $A.$ Then,

$A=\text{Area of rectangle}-\text{Area of circles}$

$=24\times 8-(3\times 3.14\times 4\times 4)$

$=192-150.72$

$=41.28c{m}^2$

$\approx 41c{m}^2$

Hence, the area of the shaded portion is equal to $41c{m}^2.$