Question

what is the volume? 11.9 cm 17.2 cm 11.4 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.

Step2: Calculate the area of the triangular base

The base is a triangle with base $b = 11.9$ cm and height $h_{triangle}=11.4$ cm. The area of a triangle is $B=\frac{1}{2}bh$. So, $B=\frac{1}{2}\times11.9\times11.4=\frac{11.9\times11.4}{2}=\frac{135.66}{2}=67.83$ $cm^{2}$.

Step3: Calculate the volume of the prism

The height of the prism $h = 17.2$ cm. Using the volume formula $V = Bh$, we substitute $B = 67.83$ $cm^{2}$ and $h = 17.2$ cm. So, $V=67.83\times17.2 = 1166.676$ $cm^{3}$.

Answer:

$1166.676$