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

$Hypotenuse=\sqrt{225}$

$Hypotenuse=15$

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.

$A=(9+12+15)\times 6$

$A=(36)\times 6$

$A=216$

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