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

Answer 1

To find the surface area of a rectangular pyramid, we need to find the areas of the base and the four triangular faces and then add them together.

The area of the rectangular base is length times width: $15\text{ m}\times 12\text{ m} = 180\text{ m}^2$.

The area of each triangular face is $1/2$ times the base times the height. Since the base of each of the four triangular faces is 12 m (this is the length of the rectangular base), the area of each triangular face is $1/2\times 12\text{ m}\times 10\text{ m} = 60\text{ m}^2$.

Therefore, the total surface area of the rectangular pyramid is $180\text{ m}^2 + 4\cdot 60\text{ m}^2 = 180\text{ m}^2 + 240\text{m}^2 = 420\text{ m}^2$.

The surface area of the rectangular pyramid is $\boxed{420}$ square meters.