find the surface area of a rectangular pyramid with these measurements. l=15m , 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 the base and the area of each triangular face.

The base of the pyramid is a rectangle, with length (l) of 15m and width (w) of 12m. Therefore, the area of the base is A_base = l * w = 15m * 12m = 180m^2.

Next, we need to find the areas of the triangular faces. The height (h) of the pyramid is 10m.

To find the area of a triangular face, we can use the formula A_triangle = (1/2) * base * height. Since the base of each triangular face is equal to the length or width of the base rectangle (15m or 12m), we can use these values to calculate the areas of the triangular faces:

A_triangle1 = (1/2) * 15m * 10m = 75m^2
A_triangle2 = (1/2) * 12m * 10m = 60m^2
A_triangle3 = (1/2) * 15m * 10m = 75m^2
A_triangle4 = (1/2) * 12m * 10m = 60m^2

Lastly, we add up the areas of the base and the four triangular faces to find the total surface area of the rectangular pyramid:

Surface area = A_base + A_triangle1 + A_triangle2 + A_triangle3 + A_triangle4
Surface area = 180m^2 + 75m^2 + 60m^2 + 75m^2 + 60m^2
Surface area = 450m^2

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