Question

Please help me out please

Answer 1

48 ft³

Explanation:

The volume (V) of the pyramid is

V =
`(1)/(3)` 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 =
`√(16)` = 4

area of square base = 6² = 36, hence

V =
`(1)/(3)` × 36 × 4 = 12 × 4 = 48 ft³