a right triangular prism with an equilateral triangular base is shown. the height of the right triangular prism is equal to 7 feet (ft), and each side of the triangular base has length 5 ft. what is the volume of the right triangular prism, rounded to the nearest cubic foot (ft³)?

Question

Accepted Answer

# Explanation:
## Step1: Calculate the area of the equilateral triangle base
The formula for the area of an equilateral triangle with side length $a$ is $A=\frac{\sqrt{3}}{4}a^{2}$. Here $a = 5$ ft.
$$
\begin{align*}
A&=\frac{\sqrt{3}}{4}\times5^{2}\
&=\frac{25\sqrt{3}}{4}\text{ ft}^{2}
\end{align*}
$$
## Step2: Calculate the volume of the prism
The formula for the volume of a prism is $V=Ah$, where $A$ is the area of the base and $h$ is the height of the prism. Here $h = 7$ ft.
$$
\begin{align*}
V&=\frac{25\sqrt{3}}{4}\times7\
&=\frac{175\sqrt{3}}{4}\
&\approx\frac{175\times1.732}{4}\
&=\frac{303.1}{4}\
& = 75.775\approx76\text{ ft}^{3}
\end{align*}
$$

# Answer:
$76$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the area of the equilateral triangle base

Step2: Calculate the volume of the prism

Answer: