Question

Determine the area of this shape. Express your answer in terms of pi.

Answer 1

The area of the composite shape is $21\pi\text{ sq. units}$

The shape is made up of four semi-circular regions. (see image attached to the solution). The area can be computed as follows:

$Area=(A-C)+(B-D)$

where each letter represents the areas of the associated semi-circles.

The area of a semi-circle is given by

$Area_s=\dfrac{\pi r^2}{2}$

For region $A$, $r=6units$

$A=\dfrac{\pi\times6^2}{2}\\\\=18\pi \text{ sq.units}$

For region $B$, $r=4units$

$B=\dfrac{\pi\times4^2}{2}\\\\=8\pi \text{ sq.units}$

For region $C$, $r=3units$

$C=\dfrac{\pi\times3^2}{2}\\\\=4.5\pi \text{ sq.units}$

For region $D$, $r=1units$

$D=\dfrac{\pi\times1^2}{2}\\\\=0.5\pi \text{ sq.units}$

So, the area of the shape is

$Area=(A-C)+(B-D)\\\\=[(18-4.5)+(8-0.5)]\pi\\\\=21\pi\text{ sq.units}$

Learn more about how to compute the area of composite shapes: brainly.com/question/316492