Question

Find the lateral surface area of a triangular prism with height of 6 inches and right triangles bases with legs 9 inches and 12 inches

Answer 1

Given:

Height of a triangular prism = 6 inches

Legs of right triangular base are 9 inches and 12 inches.

To find:

The lateral surface area of a triangular prism.

Solution:

According to the Pythagoras theorem:

`Hypotenuse^2=Base^2+Perpendicular^2`

Using Pythagoras theorem, we get

`Hypotenuse^2=(9)^2+(12)^2`

`Hypotenuse^2=81+144`

`Hypotenuse^2=225`

Taking square root on both sides, we get

`Hypotenuse=√(225)`

`Hypotenuse=15`

Now, the lateral surface area of a triangular prism.

`A=Ph`

Where, P is the perimeter of the base and h is the height of the prism.

`A=(9+12+15)* 6`

`A=(36)* 6`

`A=216`

Therefore, the lateral surface area of a triangular prism is 216 square inches.