A regular right square pyramid has a base side of 14 cm. An ant walks from one corner of the base to the midpoint of the slant edge opposite that corner by the shortest surface path. If the pyramid's perpendicular height is 9 cm, find the lateral surface area.
Show answer & explanation
Correct answer: C
Explanation
Given:
Side of the base = 14 cm
Height = 9 cm
According to the formula:
Slant height = √(h² + (a/2)²)
Area of one triangular face = 1/2 × a × l
l = √(9² + 7²)
= √(81 + 49)
= √130
= 11.4
Area of one triangular face = 1/2 × 14 × 11.4 = 79.8 cm²
Area of the four triangular faces = 4 × 79.8 = 319.25 cm²