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. (1 point)
Box m ^ 2
The surface area of a rectangular pyramid can be calculated by finding the area of the base and adding it to the sum of the areas of the four triangular faces.
The area of the base is given by the formula: A(base) = l * w
In this case, l = 15m and w = 12m, so the area of the base is: A(base) = 15m * 12m = 180m^2
To find the area of each triangular face, we can use the formula: A(triangle) = (1/2) * base * height
In this case, the height of the pyramid (h) is given as 10m, and the base of each triangular face can be calculated as follows:
- For the first triangular face, the base is equal to the length of the base of the rectangular pyramid, l = 15m.
- For the other three triangular faces, the base is equal to the width of the base of the rectangular pyramid, w = 12m.
So, for the first triangular face, the area is: A(triangle1) = (1/2) * l * h = (1/2) * 15m * 10m = 75m^2
And for the other three triangular faces, the area is: A(triangle2) = A(triangle3) = A(triangle4) = (1/2) * w * h = (1/2) * 12m * 10m = 60m^2
Therefore, the total surface area of the rectangular pyramid is the sum of the area of the base and the areas of the four triangular faces:
Surface area = A(base) + A(triangle1) + A(triangle2) + A(triangle3) + A(triangle4)
Surface area = 180m^2 + 75m^2 + 60m^2 + 60m^2 + 60m^2
Surface area = 435m^2
Hence, the surface area of the rectangular pyramid is approximately 435 m^2 rounded to the nearest hundredth.