find the surface area of a rectangular pyramid with these measurements: I = 15 m, w = 12 m, and h = 10 m. Express your answer as a decimal rounded to the nearest hundredth.
To find the surface area of a rectangular pyramid, we need to find the area of each face and then add them together.
The rectangular pyramid has a base with length 15 m and width 12 m, so the area of the base is 15 * 12 = 180 square meters.
There are four triangular faces, each with a base equal to the width of the base rectangle and a height equal to the slant height of the pyramid. The slant height can be found using the Pythagorean theorem, which states that the square of the hypotenuse (the slant height in this case) is equal to the sum of the squares of the other two sides.
In this case, the two other sides are the height of the pyramid (10 m) and half the width of the base rectangle (6 m).
So, the slant height is sqrt(10^2 + 6^2) = sqrt(136) ≈ 11.66 m.
Each triangular face has an area of (1/2)*(12 m)*(11.66 m) = 69.96 square meters.
Therefore, the total surface area of the rectangular pyramid is 180 + 4(69.96) = 459.84 square meters.
Rounded to the nearest hundredth, the surface area of the pyramid is 459.84 square meters.