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?(1 point)
Responses
202 ft.2
202 ft. squared
126 ft.2
126 ft. squared
70 ft.2
70 ft. squared
196 ft.2
To calculate the surface area of a rectangular pyramid, we need to find the area of the base and the area of the 4 triangular faces.
Area of the base = 10 ft x 7 ft = 70 ft^2
To find the area of the triangular faces, we will use the slant height and the base of each triangle:
For the triangle with slant height 7 ft:
Area = 1/2 x base x height = 1/2 x 10 ft x 7 ft = 35 ft^2
For the triangle with slant height 8 ft:
Area = 1/2 x base x height = 1/2 x 7 ft x 8 ft = 28 ft^2
Now we find the total surface area:
70 ft^2 (base) + 2(35 ft^2) + 2(28 ft^2) = 70 ft^2 + 70 ft^2 + 56 ft^2 = 196 ft^2
Therefore, the correct calculation for the surface area of the pyramid is 196 ft^2.