Find the surface area of the rectangular pyramid with these measurements: l = 15m, w = 12m, h = 10m. Express your answer as a decimal rounded to the nearest hundredth.
The surface area of a rectangular pyramid can be found by summing the areas of each of its five faces.
The base of the pyramid is a rectangle with length l = 15m and width w = 12m. The area of the base is therefore l*w = 15m * 12m = 180m^2.
The other four faces are triangles. Each triangle has a base equal to the width of the base, which is w = 12m, and a height equal to the height of the pyramid, which is h = 10m. The area of each triangle is therefore (1/2) * w * h = (1/2) * 12m * 10m = 60m^2.
Since there are four triangular faces, the total area of the triangular faces is 4*60m^2 = 240m^2.
Summing the areas of the base and the four triangular faces gives the total surface area: 180m^2 + 240m^2 = 420m^2.
Therefore, the surface area of the rectangular pyramid is 420m^2.