find the perimeter and area of the triangle. each unit on the graph measures 1 inch. round to the nearest tenth, if necessary.
e(-2, 4)
f(-5, 0)
h(-2, 0)
g(-2, -5)
p = in.
a = in²

Question

find the perimeter and area of the triangle. each unit on the graph measures 1 inch. round to the nearest tenth, if necessary.
e(-2, 4)
f(-5, 0)
h(-2, 0)
g(-2, -5)
p =  in.
a =  in²

Accepted Answer

# Explanation:
## Step1: Calculate the length of $EF$
Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For $E(-2,4)$ and $F(-5,0)$:
$$
\begin{align*}
EF&=\sqrt{(-2 + 5)^2+(4 - 0)^2}\
&=\sqrt{3^2+4^2}\
&=\sqrt{9 + 16}\
&=\sqrt{25}\
&=5
\end{align*}
$$
## Step2: Calculate the length of $FG$
For $F(-5,0)$ and $G(-2,-5)$:
$$
\begin{align*}
FG&=\sqrt{(-5 + 2)^2+(0 + 5)^2}\
&=\sqrt{(-3)^2+5^2}\
&=\sqrt{9+25}\
&=\sqrt{34}\approx5.8
\end{align*}
$$
## Step3: Calculate the length of $EG$
For $E(-2,4)$ and $G(-2,-5)$:
$$
\begin{align*}
EG&=\sqrt{(-2+2)^2+(4 + 5)^2}\
&=\sqrt{0+81}\
&=9
\end{align*}
$$
## Step4: Calculate the perimeter $P$
$P=EF + FG+EG$. Substitute the values: $P = 5+5.8 + 9=19.8$
## Step5: Calculate the area $A$
The base $FH$: $FH=\vert-2+5\vert = 3$, the height $EH=\vert4-0\vert = 4$ and $HG=\vert0 + 5\vert=5$. The total base $b=FH+HG=3 + 5=8$, height $h = 9$ (distance between $E$ and $G$ along $x=-2$). Using the formula $A=\frac{1}{2}\times base\times height$, $A=\frac{1}{2}\times8\times9 = 36$

# Answer:
$P = 19.8$ in., $A=36$ in²

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the length of \(EF\)

Step2: Calculate the length of \(FG\)

Step3: Calculate the length of \(EG\)

Step4: Calculate the perimeter \(P\)

Step5: Calculate the area \(A\)

Answer: