Answer:
10.4 cm
Step-by-step explanation:
The volume (V) of a pyramid is calculated using
V = [tex]\frac{1}{3}[/tex] area of base × height (h)
area of square base = 6² = 36, thus
[tex]\frac{1}{3}[/tex] × 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 = [tex]\sqrt{109}[/tex] ≈ 10.4 cm
