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

The formula to calculate the surface area of a triangular prism is:
Surface Area = 2 * base area + lateral area

The base of the triangular prism is a triangle. Let's assume the base of the triangular prism has sides of length a, b, and c. The area of a triangle can be calculated using Heron's formula:
s = (a + b + c) / 2
Area = √[s(s-a)(s-b)(s-c)]

Let's assume the dimensions of the triangular prism are:
a = 3 cm
b = 4 cm
c = 5 cm
height = 6 cm

Using these values, we can calculate the surface area of the triangular prism:
s = (3 + 4 + 5) / 2 = 6
Area = √[6(6-3)(6-4)(6-5)] = √[6*3*2*1] = √[36] = 6 cm^2

Base area = Area of triangle = 6 cm^2
Lateral area = perimeter of base * height = (3 + 4 + 5) * 6 = 36 cm^2

Surface Area = 2 * base area + lateral area
Surface Area = 2 * 6 + 36
Surface Area = 12 + 36
Surface Area = 48 cm^2

Therefore, approximately 48 square cm of wrapping paper is needed to wrap the toy.