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 hundreth.
To find the surface area of a rectangular pyramid, we need to find the area of each face and then add them up.
The base of the pyramid is a rectangle with length l = 15 m and width w = 12 m. So, the area of the base is A_base = l * w = 15 * 12 = <<15*12=180>>180 m^2.
The other four faces of the pyramid are triangles with the same base as the rectangle and height h = 10 m.
Each triangle has a base b = 15 m and height h = 10 m, so the area of each triangle is A_tri = (1/2) * b * h = (1/2) * 15 * 10 = 75 m^2.
Since there are four of these triangular faces, the total area of these triangular faces is 4 * A_tri = 4 * 75 = 300 m^2.
Now, we can calculate the total surface area by adding the area of the base and the area of the triangular faces:
Total surface area = A_base + Total area of triangular faces
= 180 + 300
= 480 m^2
Therefore, the surface area of the rectangular pyramid is 480 square meters.