Question

Find the surface area of a rectangular pyramid with these measurement l=13 w=11 h=8

Answer 1

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

1. Base:
The base of the pyramid is a rectangle with length l=13 and width w=11.
Area of the base = l * w = 13 * 11 = 143 square units.

2. Side faces:
The side faces of the pyramid are isosceles triangles. To calculate their areas, we need to find the slant height first.
The slant height can be calculated using the Pythagorean theorem:
slant height² = (l/2)² + h²
slant height² = (13/2)² + 8²
slant height² = (169/4) + 64
slant height² = 169/4 + 256/4
slant height² = 425/4
slant height = √(425/4)
slant height ≈ 10.303

Area of one side face = (1/2) * base * height
Area of one side face = (1/2) * l * slant height
Area of one side face = (1/2) * 13 * 10.303
Area of one side face ≈ 66.899 square units.

3. There are 4 side faces in total, so the total area of the side faces is 4 * 66.899 = 267.596 square units.

Total surface area = Area of base + Total area of side faces
Total surface area = 143 + 267.596
Total surface area ≈ 410.596 square units.

Therefore, the surface area of the given rectangular pyramid is approximately 410.596 square units.