Question

Find the surface area of a rectangular Pyramid with these measurements: j=8yd., w=4yd., and h=2yd

Answer 1

The surface area of a rectangular pyramid is calculated by adding the area of the base to the combined area of the four triangular faces.

First, calculate the area of the base:
Area of base = length × width = 8yd × 4yd = 32yd²

Next, calculate the area of each triangular face:
For the first triangular face, the base is the width of the base and the height is the height of the pyramid.
Area of first triangular face = (1/2) × width × height = (1/2) × 4yd × 2yd = 4yd²

For the second triangular face, the base is the length of the base and the height is the height of the pyramid.
Area of second triangular face = (1/2) × length × height = (1/2) × 8yd × 2yd = 8yd²

For the third triangular face, the base is the width of the base and the height is the slant height of the pyramid.
The slant height can be calculated using the Pythagorean theorem: slant height² = height² + (width/2)²
slant height² = 2yd² + (4yd/2)²
slant height² = 2yd² + 2yd²
slant height² = 4yd²
slant height = 2yd
Area of third triangular face = (1/2) × width × slant height = (1/2) × 4yd × 2yd = 4yd²

For the fourth triangular face, the base is the length of the base and the height is the slant height of the pyramid.
Area of fourth triangular face = (1/2) × length × slant height = (1/2) × 8yd × 2yd = 8yd²

Finally, add the area of the base and the combined area of the four triangular faces to find the total surface area:
Surface area = Area of base + Area of first triangular face + Area of second triangular face + Area of third triangular face + Area of fourth triangular face
Surface area = 32yd² + 4yd² + 8yd² + 4yd² + 8yd²
Surface area = 56yd² + 12yd²
Surface area = 68yd²

The surface area of the rectangular pyramid is 68yd².