A restaurant uses a container that is shaped like a right triangular prism to package carry out sandwich orders. A net of the container is shown below.
Note: Figure is not drawn to scale.
What is the surface area of the container?
To find the surface area of the container, we need to find the area of each face of the triangular prism and then add them all up.
1. The two triangular faces have a base of 6 inches and a height of 8 inches.
Area of one triangular face = 1/2 * base * height = 1/2 * 6 * 8 = 24 square inches
Since there are two triangular faces, the total area for both triangular faces = 2 * 24 = 48 square inches
2. The three rectangular faces have dimensions:
- Front face: 6 inches by 8 inches
- Side face 1: 6 inches by 8 inches
- Side face 2: 6 inches by 10 inches
Area of front face = 6 * 8 = 48 square inches
Area of side face 1 = 6 * 8 = 48 square inches
Area of side face 2 = 6 * 10 = 60 square inches
Total area for all three rectangular faces = 48 + 48 + 60 = 156 square inches
Therefore, the total surface area of the container = area of triangular faces + area of rectangular faces
= 48 + 156
= 204 square inches
So, the surface area of the container is 204 square inches.