Answer:
[tex]73 in.^2[/tex]
Step-by-step explanation:
The figure shown here consists of two pieces:
- A hemicircle
- A triangle
So, the total area of the figure is the sum of the areas of the two parts.
The area of the hemicircle is given by:
[tex]A_1=\frac{\pi r^2}{2}[/tex]
where
r = 4 in. is the radius (half the diameter, which is 8 inches)
Therefore,
[tex]A_1=\frac{\pi (4)^2}{2}=25.1 in.^2[/tex]
The area of the triangle is given by
[tex]A_2=\frac{1}{2}bh[/tex]
where
b is the base
h is the height
Here we have:
h = 8 in. is the height
The base is the total length (16 in.) minus the radius of the circle, so
[tex]b=16 - 4 = 12 in.[/tex]
So the area of the triangle is
[tex]A_2=\frac{1}{2}(12)(8)=48 in.^2[/tex]
So the total area of the figure is
[tex]A=A_1+A_2=25 in^2 + 48 in^2 = 73 in.^2[/tex]
