what is the area of the figure? round to the nearest centimeter.
a. 41 cm²
b. 55 cm²
c. 82 cm²
d. 167 cm²

Question

Accepted Answer

# Explanation:
## Step1: Calculate the area of the semicircle
The formula for the area of a circle is $A = \pi r^{2}$. For a semicircle, the area $A_{semicircle}=\frac{1}{2}\pi r^{2}$. Given the diameter $d = 6$ cm, the radius $r=\frac{d}{2}=3$ cm.
$$
\begin{align*}
A_{semicircle}&=\frac{1}{2}\times\pi\times(3)^{2}\
&=\frac{9\pi}{2}\
&\approx\frac{9\times3.14}{2}\
& = 14.13\space cm^{2}
\end{align*}
$$
## Step2: Calculate the area of the triangle
The formula for the area of a triangle is $A=\frac{1}{2}bh$. The base $b = 6$ cm. The height $h=9 - 3=6$ cm (since the radius of the semicircle is 3 cm).
$$
\begin{align*}
A_{triangle}&=\frac{1}{2}\times6\times6\
&= 18\space cm^{2}
\end{align*}
$$
## Step3: Calculate the total area of the figure
$$
\begin{align*}
A_{total}&=A_{semicircle}+A_{triangle}\
&=14.13 + 27\
&=41.13\space cm^{2}\approx41\space cm^{2}
\end{align*}
$$

# Answer:
A. $41\space cm^{2}$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the area of the semicircle

Step2: Calculate the area of the triangle

Step3: Calculate the total area of the figure

Answer: