A rectangular pyramid has a base with sides 10 ft. and 7 ft. The slant height where the base has the longer side is 7 ft., and the slant height where the base has the shorter side is 8 ft. Which of the following correctly calculates the surface area of the pyramid?
A. 202 ft.^2
B. 196 ft.^2
C. 126 ft.^2
D. 70 ft.^2
B. 196 ft.^2
To calculate the surface area of a rectangular pyramid, you would add the area of the base to the sum of the areas of the four triangular faces.
First, calculate the base area: 10 ft. * 7 ft. = 70 ft.^2
Next, calculate the area of the four triangular faces:
- Two triangles with base 10 ft. and slant height 7 ft.
Area = 1/2 * base * height = 1/2 * 10 ft. * 7 ft. = 35 ft.^2 each
- Two triangles with base 7 ft. and slant height 8 ft.
Area = 1/2 * base * height = 1/2 * 7 ft. * 8 ft. = 28 ft.^2 each
Now, calculate the total surface area:
70 ft.^2 (base) + 35 ft.^2 + 35 ft.^2 + 28 ft.^2 + 28 ft.^2 = 196 ft.^2
Therefore, the correct answer is B. 196 ft.^2.