Answer:
129.1 square units
Step-by-step explanation:
First, let's find the area of the rectangle. We can use the formula below.
[tex]a=lw[/tex]
where [tex]l[/tex] is the length and [tex]w[/tex] is the width.
The length of the rectangle is 13 and the width is 8.
[tex]l=13\\w=8[/tex]
Substitute the values into the formula.
[tex]a=13*8[/tex]
[tex]a=104[/tex]
Next, let's find the area of the semicircle. We can use the formula below.
[tex]a=\frac{1}{2} *\pi r^2[/tex]
First, find the radius. The radius is half of the diameter, and the diameter is 8.
⇒ r= d/2
⇒ r= 8/2
⇒ r= 4
[tex]a=\frac{1}{2} *\pi (4)^2[/tex]
Evaluate the exponent.
⇒ 4² = 4*4 = 16
[tex]a=\frac{1}{2} *\pi *16[/tex]
Multiply pi and 16.
[tex]a=\frac{1}{2} *50.2654825[/tex]
Multiply.
[tex]a=25.1327412[/tex]
Finally, find the area of the figure.
Add the area of the rectangle (104) and the area of the semicircle (25.1327412)
[tex]104+25.1327412[/tex]
[tex]129.132741[/tex]
Round to the nearest tenth. The 3 in the hundredth place tells us to leave the 1 in the tenth place.
[tex]129.1[/tex]
The area of the figure is about 129.1 (square units).
