Answer:
48 ft³
Step-by-step explanation:
The volume (V) of the pyramid is
V = [tex]\frac{1}{3}[/tex] area of base × perpendicular height (h)
Calculate h using the right triangle formed by a segment from the vertex to the midpoint of the base and across to the slant face ( the hypotenuse )
Using Pythagoras' identity on the right triangle then
h² + 3² = 5²
h² + 9 = 25 ( subtract 9 from both sides )
h² = 16 ( take the square root of both sides )
h = [tex]\sqrt{16}[/tex] = 4
area of square base = 6² = 36, hence
V = [tex]\frac{1}{3}[/tex] × 36 × 4 = 12 × 4 = 48 ft³
