A right triangular prism is constructed so that it's height is equal to the leg length of the base. What expression represents the volume of the prism, in cubic units? A. 1…

Question

asked Jan 8, 2021 173k views

2 Answers

Jperras · Answer 1 · 2021-01-11T22:16:53+0000

Answer:

A)
(1)/(2)x^3

Explanation:

The volume of a triangular prism can be found using the formula

V=Ah (1)

where

A is the area of the base

h is the height of the prism

Here, the base is a right triangle; the area of a triangle is

A=(1)/(2)bh'

where

b is the base

h' is the height of the triangle

Here, the triangle has the two sides equal, and it is a right triangle, so we have

b=h=x

So the area of the base is

$A=(1)/(2)x\cdot x = (1)/(2)x^2$

We also know that the height of the prism is equal to the leg length of the base, so

h=x

Therefore substituting into (1) we find:

$V=(1)/(2)x^2 \cdot x = (1)/(2)x^3$