Question

What is the surface area of a triangular prism with side lengths of 10 m, 6 m, and 12 m?

Answer 1

Based on the given dimensions, the surface area of the triangular prism is 396
`m^2`.

How to calculate surface area of a triangular prism

Given the side lengths of the triangular prism are 10 m, 6 m, and 12 m:

The triangular base has sides of 10 m and 6 m.

The height of the prism is 12 m.

Calculate the area of one triangular base:

Area of a triangle = (1/2) * base * height

Area = (1/2) * 10 m * 6 m

Area = 30
`m^2`

Calculate the area of the other triangular base (it's the same size as the first one):

Area = 30
`m^2`

Calculate the lateral surface area:

The lateral faces are rectangles, and their area is the perimeter of the base triangle multiplied by the height of the prism.

Perimeter of the base triangle = 10 m + 6 m + 12 m = 28 m

Lateral surface area = Perimeter * Height = 28 m * 12 m = 336
`m^2`

Calculate the total surface area:

Total surface area = 2 * Area of one triangular base + Lateral surface area

Total surface area = 2 * 30
`m^2` + 336
`m^2`

Total surface area = 60 s
`m^2` + 336
`m^2`

Total surface area = 396
`m^2`

Therefore, the surface area of the triangular prism is 396
`m^2`.