if the height of a square pyramid is 132 m and the base is 85 what is the slant height
To find the slant height of a square pyramid, we can use the Pythagorean theorem.
Consider a right triangle with the height of the pyramid as one leg, the slant height as the hypotenuse, and half of the base (which is half of the square's side length that forms the base of the pyramid) as the other leg.
Let's call the slant height "s", the height "h", and the base "b".
Using the Pythagorean theorem, we have:
s² = h² + (b/2)²
Plugging in the given values, we have:
s² = 132² + (85/2)²
s² = 17424 + 722.5
s² = 18146.5
To find s, we take the square root of both sides:
s = √(18146.5)
s ≈ 134.87
Therefore, the slant height of the square pyramid is approximately 134.87 m.