Question

the volume of this triangular prism is 19,188 cubic centimeters. what is the value of g? 36.9 cm g 26 cm g = centimeters

Explanation:

Step1: Recall volume formula for triangular prism

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 base length $26$ cm and height $g$, so $B=\frac{1}{2}\times26\times g = 13g$. The height of the prism $h = 36.9$ cm. And $V=19188$ $cm^{3}$.

Step2: Substitute values into formula

We substitute into $V = Bh$: $19188=13g\times36.9$.

Step3: Solve for $g$

First, simplify the right - hand side: $13g\times36.9 = 479.7g$. Then, solve the equation $479.7g=19188$ for $g$. Divide both sides by $479.7$: $g=\frac{19188}{479.7}=40$.

Answer:

$40$