Question

A tent company has a tent design that is a triangular prism. The following is a net of the design.



Note: Figure is not drawn to scale.

If a = 75 inches, b = 76 inches, c = 40 inches, and d = 72 inches, how much fabric is needed to make the tent?

Answer 1

To calculate the amount of fabric needed to make the tent, we need to find the surface area of the triangular prism.

The surface area of a triangular prism is calculated using the formula:

Surface Area = (2 * area of triangle base) + (perimeter of base * height)

First, we need to find the area of the triangle base. We will use the formula:

Area = 0.5 * base * height

In this case, the base of the triangle is side a, and the height of the triangle is c. So,

Area of triangle base = 0.5 * 75 * 40 = 1500 square inches

Next, we need to find the perimeter of the base, which is the sum of all three sides of the triangle.

Perimeter of base = a + b + c = 75 + 76 + 40 = 191 inches

Now, we can calculate the surface area of the triangular prism:

Surface Area = (2 * area of triangle base) + (perimeter of base * height)
Surface Area = (2 * 1500) + (191 * 72)
Surface Area = 3000 + 13752
Surface Area = 16752 square inches

Therefore, 16752 square inches of fabric is needed to make the tent.