Question

In the figure, assume that angles that appear to be right angles are right angles.What is the area of the figure?Use 3.14 for π.The approximate area is ___ square units.Use 3.14 for π.

Answer 1

We can break apart the figure into a half-circle, rectangle, and a triangle.

Shown below:

We find the area of each region and sum it up to find the area of the total figure.

Area of Half Circle

The volume of the area of a half circle is

$A=\frac{\pi r^2}{2}$

Given, radius (r) = 3, we find the area:

$\begin{gathered} A=\frac{\pi r^2^{}}{2} \\ A=\frac{\pi(3)^2}{2} \\ A=\frac{9\pi}{2} \\ A=\frac{9(3.14)}{2} \\ A=14.13 \end{gathered}$

Area of Rectangle

The area of a rectangle is found by multiplying the length and width.

Given,

Length = 8

Width = 6

The area is:

$\begin{gathered} A=8\times6 \\ A=48 \end{gathered}$

Area of Triangle

The area of a triangle is given by the formula,

$A=\frac{1}{2}bh$

Where

b is the base length and h is the height

Given,

b = 3

h = 6

The area of the triangle is,

$\begin{gathered} A=\frac{1}{2}bh \\ A=\frac{1}{2}(3)(6) \\ A=9 \end{gathered}$

The total area of the figure >>>

14.13 + 48 + 9

= 71.13 square units