Question

the volume of this triangular prism is 4,953.3 cubic centimeters. what is the value of t? 30 cm t 20.9 cm t = centimeters

Explanation:

Step1: Recall volume formula

The volume formula for a triangular prism is $V = Bh$, where $B$ is the area of the base and $h$ is the height of the prism. The base is a triangle with area $B=\frac{1}{2}\times t\times30$, and the height of the prism $h = 20.9$. So $V=\frac{1}{2}\times t\times30\times20.9$.

Step2: Substitute given values

We know that $V = 4953.3$. Substitute into the formula: $4953.3=\frac{1}{2}\times t\times30\times20.9$.

Step3: Simplify the right - hand side

First, calculate $\frac{1}{2}\times30\times20.9 = 313.5$. So the equation becomes $4953.3 = 313.5t$.

Step4: Solve for t

Divide both sides of the equation by 313.5: $t=\frac{4953.3}{313.5}$.
$t = 15.8$.

Answer:

$15.8$