Question

A right triangular prism has lateral area 120 cm². If the base edges are 4 cm, 5 cm and 6 cm long, find the height of the prism.

Short answer

The height of the prism is8 cm.

Step-by-step solution

Step 1. Given information.

The base edges of a right triangular prism are $4\text{cm,\hspace{0.17em}\hspace{0.17em}5cm,\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}6cm}$and lateral area is$120{\text{cm}}^2$ .

Step 2. Write the concept.

The lateral area of the prism is given by:

$\text{L.A.}=\text{Perimeter}\times \text{Height}$

Step 3. Determine the height.

Substitute the given values in the formula:

$\begin{array}{c}\text{L.A}.=(4+5+6)\left(h\right)\\ 120=\left(15\right)\left(h\right)\text{[add]}\\ h=8\text{\hspace{0.17em}cm[multiply]}\end{array}$