Note: Figure not drawn to scale
Lengths have been rounded for computational ease.
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, we need to calculate the area of each of the five faces and then sum them up.
1. The base of the pyramid is a rectangle with dimensions W by X:
Area of the base = W * X = 13 * 5 = 65 square units
2. The four triangular faces are congruent to each other. To find the area of one triangular face, we can use the formula for the area of a triangle, which is 1/2 * base * height. The base of each triangle is W (13 units) and the height is Y (9 units):
Area of one triangular face = 1/2 * 13 * 9 = 58.5 square units
We have four of these triangular faces, so the total area of the four triangular faces is:
Total area of the four triangular faces = 4 * 58.5 = 234 square units
3. Now, we sum up the area of the base and the four triangular faces to get the total surface area of the pyramid:
Total surface area = Area of the base + Total area of the four triangular faces
Total surface area = 65 + 234 = 299 square units
Therefore, the surface area of the right rectangular pyramid is 299 square units. So the correct answer is:
299 square units