Question

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. 1/2x^3 B. 1/2x^2+x C. 2x^3 D. 2x^2+x

Answer 1

A

Explanation:

Answer 2

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`