Question

Please help me out with this

Answer 1

Answer:

10.4 cm

Step-by-step explanation:

The volume (V) of a pyramid is calculated using

V = $\frac{1}{3}$ area of base × height (h)

area of square base = 6² = 36, thus

$\frac{1}{3}$ × 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 = $\sqrt{109}$ ≈ 10.4 cm