find the surface area of a rectangular pyramid with these measurements L=15m,W=12m and H=10m. 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 the base and the area of the four triangular faces.
The area of the base of the rectangular pyramid is given by the formula: L * W, where L is the length and W is the width.
So, the area of the base is: 15m * 12m = 180m².
The area of each triangular face can be found by multiplying the base of the triangle by the height and dividing the result by 2.
The base of each triangular face is the same as the length of the base of the pyramid, which is 15m.
The height of each triangular face is the slant height (s), which can be calculated using the Pythagorean theorem. Given that the height of the pyramid (H) is 10m, the slant height can be found using the formula: s = sqrt(L² + H²).
So, the slant height (s) is: sqrt(15² + 10²) = sqrt(225 + 100) = sqrt(325).
Now, let's calculate the area of one triangular face:
Area = (15m * sqrt(325)) / 2 ≈ 76.89m².
Since there are four triangular faces, the total area of the triangular faces is: 4 * 76.89m² = 307.56m².
Finally, we can find the surface area of the rectangular pyramid by adding the area of the base and the area of the four triangular faces:
Surface Area = 180m² + 307.56m² ≈ 487.56m².
Therefore, the surface area of the rectangular pyramid is approximately 487.56 square meters.