What is the volume of a square peer med with bass edges of 40 cm at a slant height of 25 cm

The question is what is the volume of a square pyramid with base edges of 40 cm and a slant height of 25 cm.

The Volume, V,  of a pyramid is V = [1/3] * area of the base * height

The base of this pyramid is a square of side 40 cm, then its area is (40cm)^2 = 1600 cm^2

The height of the pyramid is calculated using Pytagora's theorem:

(half side of the base)^2  + (height of the pyramid)^2 = (slant height)^2

=> (height of the pyramid)^2 = (slant height)^2 - (half side of the base)^2

(height of the pyramid)^2 = (25cm)^2 - (20cm)^2 = 225 cm^2

=> height of the pyramid = 15 cm

Now you can calcualte the volume of the pyramid with the formula V = [1/3](area of the base)(height)

V = [1/3](1600 cm^2)(15 cm) =   8000 cm^3

8000 cm^3