Find the surface area of the rectangular pyramid with these measurements: l = 14 m, w = 10 m, and h = 15 m

Question

Round the answer to the nearest hundredth (Keep in mind you have the height, not the slant height)

Answer 1

To find the surface area of a rectangular pyramid, you need to calculate the areas of the base and the four triangular faces.

The area of the base can be found by multiplying the length and width of the base:
Area of the base = l * w = 14 m * 10 m = 140 m².

The area of each triangular face can be found using the formula for the area of a triangle:
Area of a triangle = (1/2) * base * height.

Since the base of each triangular face is given by the length or width of the rectangular base of the pyramid, and the height is given as 15 m, the formula becomes:
Area of each triangular face = (1/2) * l * h = (1/2) * 14 m * 15 m = 105 m².

Since the pyramid has four triangular faces, the total area of the four triangular faces is:
Total area of four triangular faces = 4 * Area of each triangular face = 4 * 105 m² = 420 m².

Thus, the total surface area of the rectangular pyramid is:
Total surface area = Area of the base + Total area of four triangular faces
= 140 m² + 420 m² = 560 m².

Therefore, the surface area of the rectangular pyramid is 560 square meters.