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.(1 point)

The surface area of a rectangular pyramid can be calculated by finding the area of each face and summing them up.

The base of the pyramid is a rectangle with dimensions 15 m and 12 m, so the area of the base is 15 * 12 = 180 m^2.

The lateral faces of the pyramid are all triangles. To find their areas, we need to find the length of the slant height (s). This can be found using the Pythagorean theorem.

First, let's find the height of each triangle. The height (h) is given as 10 m.

Next, let's find the length of each side of the base of the triangle. The base of the triangle is 12 m, so the hypotenuse of each triangle is 15 m.

Using the Pythagorean theorem, we can find s:

s = sqrt(h^2 + (1/2 * base)^2)
s = sqrt(10^2 + (1/2 * 12)^2)
s = sqrt(100 + 36)
s = sqrt(136)
s ≈ 11.66 m

The area of each lateral face is (1/2) * base * height, which is (1/2) * 12 * 11.66 = 70 m^2.

Since there are four lateral faces, the total area of the lateral surfaces is 4 * 70 = 280 m^2.

Finally, the total surface area of the rectangular pyramid is the sum of the base area and the lateral surface area: 180 + 280 = 460 m^2.

Therefore, the surface area of the rectangular pyramid is 460 m^2.

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