Question

If the volume of the triangular prism shown in the given image is 684 cubic centimeters, what will its length be?

• A. $30cm$
• B. $32cm$
• C. $36cm$
• D. $35cm$

Answer 1

The correct option is A $30cm$

Base length of the triangle of the prism $=9.5cm$
Height of the triangle of the prism $=4.8cm$
Area of the triangular base $=\frac{1}{2}\times \text{base}\times \text{height}$
$=\frac{1}{2}\times 9.5\times 4.8$
$=\frac{1}{2}\times 45.6=22.8cm$

$\text{Volume of the triangular prism}=\text{area of the triangular base}\times \text{length of the prism}$
$\Rightarrow 684=22.8\times \text{length of the prism}$
$\Rightarrow \text{Length of the prism}=\frac{684}{22.8}=30cm$