Find the Volume of the triangular prism. a) a triangular prism with base 12cm, height 10cm, length 20cm. b) a triangular prism with base 8in, height 12in, length ??? . What is the Volume of a cone with a radius of 5cm and a height of 8cm?

The volume of a prism is given by the formula $V = A_{base} \times L$, where $A_{base}$ is the area of the base and $L$ is the length (or height) of the prism. For a triangular prism, the base is a triangle, and its area is $A_{triangle} = \frac{1}{2} \times base \times height$.

Given:
Base of the triangle ($b$) = $12 \text{ cm}$
Height of the triangle ($h_t$) = $10 \text{ cm}$
Length of the prism ($L$) = $20 \text{ cm}$

For question 9b, the problem asks for the volume of a triangular prism, but the accompanying diagram shows a rectangular prism. I will solve for a triangular prism, assuming the base of the triangle is $8 \text{ inches}$, the height of the triangle is $8 \text{ inches}$ (derived from the square base shown in the diagram), and the length of the prism is $12 \text{ inches}$.

Given (based on assumption for triangular prism):
Base of the triangle ($b$) = $8 \text{ in}$
Height of the triangle ($h_t$) = $8 \text{ in}$
Length of the prism ($L$) = $12 \text{ in}$