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:
[tex]Hypotenuse^2=Base^2+Perpendicular^2[/tex]
Using Pythagoras theorem, we get
[tex]Hypotenuse^2=(9)^2+(12)^2[/tex]
[tex]Hypotenuse^2=81+144[/tex]
[tex]Hypotenuse^2=225[/tex]
Taking square root on both sides, we get
[tex]Hypotenuse=\sqrt{225}[/tex]
[tex]Hypotenuse=15[/tex]
Now, the lateral surface area of a triangular prism.
[tex]A=Ph[/tex]
Where, P is the perimeter of the base and h is the height of the prism.
[tex]A=(9+12+15)\times 6[/tex]
[tex]A=(36)\times 6[/tex]
[tex]A=216[/tex]
Therefore, the lateral surface area of a triangular prism is 216 square inches.
