Question

Determine the surface area of a pyramid with a triangular base. The triangle base has two equal sides of 13 in., and the height of the base side is 12 in. The slant height of the pyramid is 7 in.(1 point)
in.2

Answer 1

First find the base triangle: the altitude 12 splits the base into two segments of length x with 13^2 = 12^2 + x^2 ⇒ x = 5, so base = 10.
Base area = (1/2)(10)(12) = 60 in^2.

Perimeter = 10 + 13 + 13 = 36 in. Lateral surface area = (1/2)(perimeter)(slant height) = (1/2)(36)(7) = 126 in^2.

Total surface area = 60 + 126 = 186 in^2.