Question

(x + 2) (x + 3) o $\frac{1}{2}x^{3}+x^{2}$ o $\frac{1}{2}x^{3}+\frac{3}{2}x^{2}$ o $x^{3}+x^{2}$ o $x^{3}+3x^{2}$

Explanation:

Step1: Find the area of the base triangle

The base is a right - angled triangle with legs of length $x$. The area of a triangle $A_{base}=\frac{1}{2}\times base\times height=\frac{1}{2}x\cdot x=\frac{1}{2}x^{2}$.

Step2: Calculate the volume of the prism

The volume of a prism $V = A_{base}\times length$. The length of the prism is $(x + 3)$. So $V=\frac{1}{2}x^{2}(x + 3)$.

Step3: Expand the expression

Using the distributive property $a(b + c)=ab+ac$, we have $V=\frac{1}{2}x^{2}\cdot x+\frac{1}{2}x^{2}\cdot3=\frac{1}{2}x^{3}+\frac{3}{2}x^{2}$.

Answer:

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