Question

Find the surface area of a rectangular pyramid with these measurements. l = 15 m, w =12 m, and. h = 10 m. Express your answer, as a decimal rounded to the nearest hundredth.

Answer 1

The surface area of a rectangular pyramid can be calculated by adding the areas of the base and the four triangular faces.

The area of the base is calculated as l * w = 15 * 12 = 180 m^2.

To calculate the area of each triangular face, we need to first find the length of the slant height (s) using the Pythagorean theorem, where s^2 = (w/2)^2 + h^2:

s^2 = (12/2)^2 + 10^2
s^2 = 6^2 + 100
s^2 = 36 + 100
s^2 = 136
s = √136
s ≈ 11.66 m

Once we have the slant height, we can calculate the area of each triangular face as (l * s) / 2 = (15 * 11.66) / 2 ≈ 174.9 m^2.

Since there are four triangular faces, the total surface area becomes:

Surface area = base area + 4 * triangular face area
Surface area = 180 + 4 * 174.9
Surface area ≈ 180 + 699.6
Surface area ≈ 879.6

Therefore, the surface area of the rectangular pyramid is approximately 879.6 square meters.