Find the surface area of a rectangular pyramid with these measurements: l = 15 m, w = 12 m, and h = 10 m. Express your answer as a decimal rounded to the nearest hundredth
The surface area of a rectangular pyramid can be found by adding the area of the base to the areas of the four triangular faces.
The area of the base is the product of the length and width: 15 m * 12 m = 180 m^2.
To find the area of each triangular face, we need to find the height of the triangles.
The height of each triangular face is the slant height of the pyramid, which can be found using the Pythagorean theorem.
In this case, the slant height can be found using the height (h) and the length (l) of the pyramid. Using the Pythagorean theorem: slant height = sqrt(h^2 + (l/2)^2).
In this case, the slant height is sqrt(10 m^2 + (15 m/2)^2) = sqrt(100 m^2 + 112.5 m^2) = sqrt(212.5 m^2).
The area of each triangular face is (1/2) * base * height, or (1/2) * (l/2) * (slant height).
Plugging in the values: (1/2) * (15 m/2) * (sqrt(212.5 m^2)) = (15/4) * sqrt(212.5) m^2.
Since there are four triangular faces, the total area of the triangular faces is 4 * (15/4) * sqrt(212.5) m^2 = 15 * sqrt(212.5) m^2.
Adding the area of the base and the area of the triangular faces, the total surface area of the pyramid is 180 m^2 + 15 * sqrt(212.5) m^2 = 180 m^2 + 15 * sqrt(212.5) m^2 ≈ 462.18 m^2.
Therefore, the surface area of the rectangular pyramid is approximately 462.18 m^2, rounded to the nearest hundredth.