Question

A triangular prism is 18 meters long and has a triangular face with a base of 12 meters and a height of 8 meters. The other two sides of the triangle are each 10 meters. What is the surface area of the triangular prism?

Answer 1

Explanation:

To find the surface area of a triangular prism, we need to add up the area of all of its faces.

First, let's calculate the area of the triangular face. The area of a triangle is given by the formula:

A = 1/2 * base * height

Plugging in the values given in the problem, we get:

A = 1/2 * 12 * 8

A = 48

So the area of the triangular face is 48 square meters.

The triangular prism has two of these faces, so the total area of the triangular faces is:

2 * 48 = 96

Next, we need to calculate the area of the rectangular faces. The rectangular faces have the same width as the base of the triangular face (12 meters), and the same height as the length of the prism (18 meters). So the area of each rectangular face is:

A = length * width

A = 18 * 12

A = 216

The triangular prism has two rectangular faces, so the total area of the rectangular faces is:

2 * 216 = 432

Finally, we add up the areas of all the faces to get the total surface area of the triangular prism:

96 + 432 = 528

Therefore, the surface area of the triangular prism is 528 square meters.