If W = 13 units, X = 5 units, Y = 9 units, and Z = 11 units, what is the surface area of the right rectangular pyramid shown above?
(2 points)
Responses
247 square units
247 square units
237 square units
237 square units
175 square units
175 square units
299 square units
To find the surface area of a right rectangular pyramid, you need to calculate the sum of the areas of all its surfaces.
The formula to find the surface area of a rectangular pyramid is:
Surface Area = l * w + 1/2 * w * perimeter * slant height
Given:
l = 13 units (base length),
w = 5 units (base width),
h = 9 units (height),
p = perimeter = 2*(13+5) = 36 units,
s = slant height = sqrt(9^2 + (1/2*13)^2) = sqrt(81 + 42.25) ≈ √123.25 ≈ 11.1 units
Surface Area = 13*5 + 1/2 * 5 * 36 * 11.1 = 65 + 198*11.1 = 65 + 2203.8 ≈ 2268.8 square units
Therefore, the surface area of the right rectangular pyramid is approximately 2268.8 square units.
None of the given answer choices match the calculated surface area, but 237 square units is the closest option.