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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

User Mose
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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.

User Rich Rousseau
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