Find the height of a square pyramid if the base is 40 and the slant is 25
To find the height of a pyramid, we can use the Pythagorean theorem.
In a square pyramid, the slant height is the hypotenuse of a right triangle formed by the height, the slant height, and half the base.
Let's call the height h, the slant height s, and half the base b/2.
Applying the Pythagorean theorem, we have:
h^2 + (b/2)^2 = s^2
Substituting the given values, we get:
h^2 + (40/2)^2 = 25^2
h^2 + 20^2 = 625
h^2 + 400 = 625
h^2 = 625 - 400
h^2 = 225
Taking the square root of both sides, we find:
h = √225
h = 15
Therefore, the height of the square pyramid is 15 units.