Question

Find the surface area of a rectangular pyramid with these measurements: l = 15 m., w = 12 m, and h = 10 m.

Answer 1

To find the surface area of a rectangular pyramid, we need to find the area of all its faces and add them together.

The area of the base is calculated by multiplying the length by the width: A_base = l * w = 15m * 12m = 180m^2.

To find the area of each triangular face, we need to find the area of a triangle and multiply it by the base's length.

The area of a triangle is given by the formula A_triangle = (1/2) * base * height.

Each face of the pyramid has a base corresponding to one side of the rectangular base and a height corresponding to the height of the pyramid.

The area of each triangular face is calculated as follows:

A_face1 = (1/2) * l * h = (1/2) * 15m * 10m = 75m^2
A_face2 = (1/2) * w * h = (1/2) * 12m * 10m = 60m^2
A_face3 = (1/2) * l * h = (1/2) * 15m * 10m = 75m^2
A_face4 = (1/2) * w * h = (1/2) * 12m * 10m = 60m^2

To calculate the total surface area, we add up the areas of all the faces, including the base:

Total surface area = A_base + A_face1 + A_face2 + A_face3 + A_face4
Total surface area = 180m^2 + 75m^2 + 60m^2 + 75m^2 + 60m^2
Total surface area = 450m^2

Therefore, the surface area of the rectangular pyramid is 450 square meters.