Find the surface area of a rectangular pyramid with these measurements length equals 8 yards with equals 4 yards and height equals 2 yards
To find the surface area of a rectangular pyramid, we need to find the areas of each face and add them together.
The formula for the surface area of a rectangular pyramid is given as:
Surface area = (l × w) + (l × √((w/2)^2 + h^2)) + (w × √((l/2)^2 + h^2))
Where:
- l = length of the rectangular base
- w = width of the rectangular base
- h = height of the pyramid
Given:
l = 8 yards
w = 4 yards
h = 2 yards
Substituting these values into the formula, we get:
Surface area = (8 × 4) + (8 × √((4/2)^2 + 2^2)) + (4 × √((8/2)^2 + 2^2))
Simplifying further:
Surface area = 32 + (8 × √(2^2 + 4)) + (4 × √(4^2 + 4))
Surface area = 32 + (8 × √(4 + 4)) + (4 × √(16 + 4))
Surface area = 32 + (8 × √(8)) + (4 × √(20))
Surface area ≈ 32 + (8 × 2.828) + (4 × 4.472)
Surface area ≈ 32 + 22.624 + 17.888
Surface area ≈ 72.512 yards^2
Therefore, the surface area of the rectangular pyramid is approximately 72.512 square yards.