Question

what is the volume? 34.6 cm 38 cm 20.6 cm cubic centimeters

Explanation:

Step1: Identify the shape as a 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, and the area of a triangle is $B=\frac{1}{2}ah$, where $a$ is the base of the triangle and $h$ is the height of the triangle.

Step2: Calculate the area of the base triangle

The base of the triangle $a = 38$ cm and the height of the triangle $h = 20.6$ cm. So, $B=\frac{1}{2}\times38\times20.6$.
$B = 19\times20.6=391.4$ $cm^{2}$.

Step3: Calculate the volume of the prism

The height of the prism $H = 34.6$ cm. Using the volume formula $V = Bh$, we substitute $B = 391.4$ $cm^{2}$ and $H = 34.6$ cm.
$V=391.4\times34.6$
$V = 13542.44$ $cm^{3}$.

Answer:

$13542.44$