Question

a right triangular prism is constructed so that its height is equal to the leg length of the base. what expression represents the volume of the prism in cubic units? options: \\(\frac{1}{2}x^3\\), \\(\frac{1}{2}x^2 + x\\), \\(2x^3\\), \\(2x^2 + x\\)

Explanation:

Step1: Find the area of the triangular base

The area formula for a triangle is $A=\frac{1}{2}\times base\times height$. For the triangular base of the prism, the base is $x$ and the height is $x$. So, $A_{base}=\frac{1}{2}\times x\times x=\frac{1}{2}x^{2}$.

Step2: Use the volume formula for a prism

The volume formula for a prism is $V = A_{base}\times h$. The height of the prism $h=x$. Substitute $A_{base}=\frac{1}{2}x^{2}$ and $h = x$ into the formula: $V=\frac{1}{2}x^{2}\times x=\frac{1}{2}x^{3}$.

Answer:

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