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
[tex]A=\frac{\pi r^2}{2}[/tex]
Given, radius (r) = 3, we find the area:
[tex]\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}[/tex]
Area of Rectangle
The area of a rectangle is found by multiplying the length and width.
Given,
Length = 8
Width = 6
The area is:
[tex]\begin{gathered} A=8\times6 \\ A=48 \end{gathered}[/tex]
Area of Triangle
The area of a triangle is given by the formula,
[tex]A=\frac{1}{2}bh[/tex]
Where
b is the base length and h is the height
Given,
b = 3
h = 6
The area of the triangle is,
[tex]\begin{gathered} A=\frac{1}{2}bh \\ A=\frac{1}{2}(3)(6) \\ A=9 \end{gathered}[/tex]
The total area of the figure >>>
14.13 + 48 + 9
= 71.13 square units
