Question

what is the volume of a triangular prism that has a width of 6 cm, height of 5 cm, and length of 7 cm?

Explanation:

Step1: Recall volume formula for triangular prism

$V = Bh$, where $B$ is the base - area and $h$ is the height of the prism. For a triangular prism with base - triangle having base $b$ and height $h_{t}$ (height of the triangle), $B=\frac{1}{2}bh_{t}$. Here, we can also use the formula $V=\frac{1}{2}\times length\times width\times height$.

Step2: Substitute given values

Given length $l = 7$ cm, width $w = 6$ cm, height $h = 5$ cm. Substitute into the formula $V=\frac{1}{2}\times l\times w\times h$.
$V=\frac{1}{2}\times7\times6\times5$

Step3: Calculate the volume

First, calculate $7\times6\times5 = 210$. Then, $\frac{1}{2}\times210=105$.

Answer:

$105$