Question

find the surface area of a rectangular pyramid with these measurements length of 15 M width 12 M and height 10 m express your answer as a decimal rounded to the nearest hundredth.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the surface area of a rectangular pyramid, we need to calculate the area of each face and then add them together.

First, let's calculate the area of the base, which is a rectangle.
The length of the base is given as 15 m and the width as 12 m.
Area of the base = length * width = 15 m * 12 m = 180 m².

Now let's calculate the areas of the four triangular faces.
We consider the height of the pyramid as the slant height of the triangles.

Area of one triangular face = (1/2) * base * height.

In this case, the base of the triangle is the same as the length of the base of the pyramid, which is 15 m.
The height of the triangle is the height of the pyramid, which is 10 m.

Area of one triangular face = (1/2) * 15 m * 10 m = 75 m².

Since there are four triangular faces, we multiply the area of one triangular face by 4 to get the total area of the four triangular faces.
Total area of the four triangular faces = 4 * 75 m² = 300 m².

Finally, to find the total surface area of the rectangular pyramid, we add the area of the base and the area of the four triangular faces.
Total surface area = Area of the base + Total area of the four triangular faces.
Total surface area = 180 m² + 300 m² = 480 m².

Therefore, the surface area of the rectangular pyramid is 480 m².