Question

charles begins finding the volume of a trapezoidal prism using the formula $a = \frac{1}{2}(b_1 + b_2)h$ to find the prism’s base area.
$a = \frac{1}{2}((x + 4) + (x + 2))x$
$a = \frac{1}{2}(2x + 6)x$
$a = (x + 3)x$
$a = x^2 + 3x$
which expression can be used to represent the volume of the trapezoidal prism?
$\boldsymbol{2x^3 + 6x^2}$
$\boldsymbol{x^3 + 6x^2}$
$\boldsymbol{x^3 + 3x^2}$
$\boldsymbol{2x^3 + 3x^2}$

Explanation:

Step1: Recall prism volume formula

Volume = Base Area × Length

Step2: Identify known values

Base Area $A = x^2 + 3x$, Length = $2x$

Step3: Calculate volume

$\text{Volume} = (x^2 + 3x) \times 2x$
$\text{Volume} = x^2 \times 2x + 3x \times 2x$
$\text{Volume} = 2x^3 + 6x^2$

Answer:

$2x^3 + 6x^2$