Question

the right triangular prism has a volume of 1,152 cm³. what is the value of x, the height of the prism? 6 8 12 16

Explanation:

Step1: Find base triangle area

The base is a right triangle with legs 12 cm each. Area formula: $\text{Area} = \frac{1}{2} \times b \times h$
$\text{Area of base} = \frac{1}{2} \times 12 \times 12 = 72 \, \text{cm}^2$

Step2: Set up volume equation

Volume of prism = (Base Area) $\times$ (Prism height $x$)
$1152 = 72 \times x$

Step3: Solve for $x$

Rearrange to isolate $x$: $x = \frac{1152}{72}$
$x = 16$

Answer:

16