Answer
Explanation
Given:
A figure based on a right triangle, a rectangle, and a semicircle.
To determine the best estimate of the figure in square centimeters, we use areas of the figures as shown below:
For right triangle:
The formula of the area is:
[tex]A=\frac{bh}{2}[/tex]
where:
b=base=12cm
h=height=12cm
A=Area
We plug in what we know:
[tex]\begin{gathered} A=\frac{bh}{2} \\ =\frac{(12)(12)}{2} \\ Simplify \\ A=72cm^2 \end{gathered}[/tex]
Hence, the area of the right triangle is 72 cm^2.
Next, we find for the area of the rectangle:
We use the formula:
[tex]A=wl[/tex]
where:
w=width=12 cm
l=length = 18 cm
So,
[tex]\begin{gathered} A=wl \\ =(12)(18) \\ Simplify \\ A=216cm^2 \end{gathered}[/tex]
Hence, the area of the rectangle is 216 cm^2.
We also find the area of the semicircle using the formula:
[tex]A=\frac{\pi r^2}{2}[/tex]
where:
r=radius = 12/2= 6cm
So,
[tex]\begin{gathered} A=\frac{\pi r^{2}}{2} \\ =\frac{\pi(6)^2}{2} \\ A=56.55cm^2 \end{gathered}[/tex]
Hence, the area of the semicircle is 56.55 cm^2.
Then, we get the total:
Total =Area of the right triangle + Area of the rectangle+ Area of the semicircle
We plug in the values:
[tex]\begin{gathered} Total\text{ Area = 72+216+56.55} \\ Calculate \\ Total\text{ Area=344.55 cm\textasciicircum2} \end{gathered}[/tex]
Therefore, the best estimate of the figure is 344.55 square centimeters.
