Question

Can anybody help me figure out the area of simple composite figure?

Answer 1

Given:

The length of the rectangle = 16 ft

The width of the rectangle = 12 ft

The diameter of the semicircle = 12 ft

To find the area of the given figure.

Formula

• $A=A_{1} +A_{2}$

where,

$A$ be the area of the given figure

$A_{1}$ be the area of the rectangle

$A_{2}$ be the area of the semicircle.

• The area of the rectangle = $lb$ where, l be the length and b be the width
• Area of the semicircle = $\frac{1}{2} \pi r^{2}$, r be the radius of the semicircle.

Now,

The radius of the semicircle r = 6 ft

Putting, r=6, l=16 and b= 12 we get,

$A_{1} = (16)(12)$ sq ft

or, $A_{1} = 192$ sq ft

$A_{2} = \frac{1}{2} (3.14)(6^{2} )$ sq ft

or, $A_{2}=56.52$ sq ft

So,

$A = 56.52+192$ sq ft

$A$ = 248.52 sq ft

Rounding off to the nearest tenth, we get;

A=248.5 sq ft.

Hence,

The area of the composite figure is 248.5 sq ft.