A net of a rectangular pyramid is shown in the figure.

Question

A net of a triangular prism with base dimensions of 6 inches by 7 inches. The larger triangular face has a height of 8 inches. The smaller triangular face has a height of 8.2 inches.

What is the surface area of the pyramid?

Answer 1

To find the surface area of the rectangular pyramid, we need to calculate the area of each individual face and then add them together.

1. Base area:
The base of the pyramid is a rectangle with dimensions 6 inches by 7 inches.
Base area = length x width = 6 inches x 7 inches = 42 square inches

2. Lateral faces:
The two lateral faces of the pyramid are triangles with base dimensions of 6 inches and 7 inches, and heights of 8 inches and 8.2 inches respectively.
Lateral face 1 area = 1/2 x base x height = 1/2 x 6 inches x 8 inches = 24 square inches
Lateral face 2 area = 1/2 x base x height = 1/2 x 7 inches x 8.2 inches = 28.7 square inches

3. Total surface area:
Surface area = base area + 2 x lateral face area
Surface area = 42 square inches + 2 x (24 square inches + 28.7 square inches)
Surface area = 42 square inches + 2 x (52.7 square inches)
Surface area = 42 square inches + 105.4 square inches
Surface area = 147.4 square inches

Therefore, the surface area of the rectangular pyramid is 147.4 square inches.