Question

8What is the lateral area of the right triangular prism?480 6096

Answer 1

To find the lateral area of a right triangular prism, apply the formula:

`LA=P\ast H`

Where:

P is the perimeter of the base

H is the height

To find the perimeter of the traingular base, apply the perimeter of a triangle formula:

P = a + b + c

Let's find the third side of the traingular base using the pythagorean theorem.

We have:

`\begin{gathered} c^2=a^2+b^2 \\ \\ c^2=4^2+3^2 \\ \\ c^2=16+9 \\ \\ c^2=25 \\ \\ \text{Take the square root of both sides:} \\ \sqrt[]{c^2}=\sqrt[]{25} \\ \\ c=5 \end{gathered}`

Thus, the perimeter of the base is:

P = 3 + 4 + 5 = 12

Hence, to find the lateral area, we have:

LA = P x H

Where:

Perimeter of base, P = 12

Height, H = 8

LA = 12 x 8 = 96

Therefore, the lateral area of the right traingular prism is 96 square units.

ANSWER:

96