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

Answer:

A) $\frac{1}{2}x^3$

Step-by-step 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

$A=\frac{1}{2}bh'$

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

$A=\frac{1}{2}x\cdot x = \frac{1}{2}x^2$

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:

$V=\frac{1}{2}x^2 \cdot x = \frac{1}{2}x^3$

Answer 2

Answer:

A

Step-by-step explanation: