Question

A toy came in a container that is shaped like a triangular prism. How much wrapping paper is needed to wrap the toy? Round your answer to the nearest whole number

Answer 1

To find the amount of wrapping paper needed, we need to calculate the surface area of the triangular prism.

The surface area of a triangular prism can be calculated using the formula:
Surface Area = 2 * base area + lateral area

First, let's calculate the base area of the triangular prism. Since the base of a triangular prism is a triangle, we can use the formula for the area of a triangle:
Area = 1/2 * base * height

Assuming the base of the triangle is 5 inches and the height of the triangle is 4 inches:
Area = 1/2 * 5 * 4 = 10 square inches

Now, let's calculate the lateral area of the triangular prism. The lateral faces of a triangular prism are three rectangles with width equal to the perimeter of the base, and height equal to the height of the prism.
Perimeter of the base = 3 * base = 3 * 5 = 15 inches

Assuming the height of the triangular prism is 6 inches:
Lateral area = 3 * 15 * 6 = 270 square inches

Now, we can calculate the total surface area of the triangular prism:
Surface Area = 2 * 10 + 270 = 20 + 270 = 290 square inches

Therefore, approximately 290 square inches of wrapping paper is needed to wrap the toy.