Question

Please help me out with this

Answer 1

10.4 cm

Explanation:

The volume (V) of a pyramid is calculated using

V =
`(1)/(3)` area of base × height (h)

area of square base = 6² = 36, thus

`(1)/(3)` × 36h = 120

12h = 120 ( divide both sides by 12 )

h = 10 cm

To find the slant height (s) consider the right triangle from the vertex to the midpoint of the base and from the midpoint of base to the side.

That is a right triangle with hypotenuse s and legs 10(h) and 3 (midpoint of the base )

Using Pythagoras' identity then

s² = 10² + 3² = 100 + 9 = 109

Take the square root of both sides

s =
`√(109)` ≈ 10.4 cm