Question

A package is in the shape of a triangular prism. The bases are right triangles with perpendicular legs measuring 9 centimeters and 12 centimeters. The distance between the bases is 10 centimeters.

What is the surface area of the triangular prism?

210 square centimeters
318 square centimeters
360 square centimeters
468 square centimeters

Answer 1

468 square centimeters

Explanation:

Answer 2

The surface area of the triangular prism is 468 square centimeters. Therefore the correct option is 4.

Explanation:

It is given that the bases are right triangles with perpendicular legs measuring 9 centimeters and 12 centimeters. Using Pythagoras theorem, the third side of the base is

`hypotenuse^2=leg_1^2+leg_2^2`

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

`hypotenuse^2=225`

`hypotenuse=√(225)`

`hypotenuse=15`

The area of a triangle is

`A=(1)/(2)* base * height`

Area of the base is

`A_1=(1)/(2)* 9* 12=54`

The curved surface area of triangular prism is

`A_2=\text{perimeter of base}* height`

`A_2=(9+12+15)* 10`

`A_2=9* 10+12* 10+15* 10`

`A_2=360`

The surface area of the triangular prism is

`A=2A_1+A_2`

`A=2(54)+360`

`A=108+360`

`A=468`

The surface area of the triangular prism is 468 square centimeters. Therefore the correct option is 4.