Find the surface area of a rectangular pyramid with these measurements:
L= 15 m, W= 12 m, H= 10 m. Express your answer as a decimal rounded to the nearest hundredth
The surface area of a rectangular pyramid can be calculated using the formula:
Surface Area = L * W + L * sqrt(((W/2)^2) + H^2) + W * sqrt(((L/2)^2) + H^2)
Plugging in the given measurements: L = 15 m, W = 12 m, H = 10 m:
Surface Area = 15 * 12 + 15 * sqrt(((12/2)^2) + 10^2) + 12 * sqrt(((15/2)^2) + 10^2)
Surface Area = 180 + 15 * sqrt(((6^2) + 100) + 12 * sqrt(((7.5^2) + 100)
Surface Area = 180 + 15 * sqrt(36 + 100) + 12 * sqrt(56.25 + 100)
Surface Area = 180 + 15 * sqrt(136) + 12 * sqrt(156.25)
Surface Area = 180 + 15 * 11.66 + 12 * 12.5
Surface Area = 180 + 174.9 + 150
Surface Area = 504.9
Therefore, the surface area of the rectangular pyramid is approximately 504.9 square meters.