find the area of the figure. round to the nearest hundredths when necessary. 7 m 9 m 16 m 16 m 16 m

Question

Accepted Answer

# Explanation:
## Step1: Calculate the area of the trapezoid
The formula for the area of a trapezoid is $A_{1}=\frac{(a + b)h}{2}$, where $a = 7\space m$, $b=16\space m$, $h = 9\space m$.
$$
\begin{align*}
A_{1}&=\frac{(7 + 16)\times9}{2}\
&=\frac{23\times9}{2}\
&=\frac{207}{2}\
& = 103.5\space m^{2}
\end{align*}
$$
## Step2: Calculate the area of the equilateral triangle
The formula for the area of an equilateral triangle is $A_{2}=\frac{\sqrt{3}}{4}s^{2}$, where $s = 16\space m$
$$
\begin{align*}
A_{2}&=\frac{\sqrt{3}}{4}\times16^{2}\
&=\frac{\sqrt{3}}{4}\times256\
&= 64\sqrt{3}\
&\approx64\times1.732\
&= 110.85\space m^{2}
\end{align*}
$$
## Step3: Calculate the total area
The total area $A=A_{1}+A_{2}$
$$
\begin{align*}
A&=103.5+110.85\
&=214.35\space m^{2}
\end{align*}
$$
# Answer:
$214.35\space m^{2}$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the area of the trapezoid

Step2: Calculate the area of the equilateral triangle

Step3: Calculate the total area

Answer: