a square pyramid's height is 15 and its base is 16. Find the slant height of the square pyramid
To find the slant height of a square pyramid, we can use the Pythagorean Theorem.
First, let's draw a diagram of the square pyramid.
The square base has side length 16 units. Let's label the center of the base as point O.
Now, connect the apex (top vertex) of the pyramid to the four corners of the square base. These lines are the slant heights of the pyramid. Let's label one of these lines as L.
We can create a right triangle using the slant height L, the height of the pyramid, and half the length of one side of the square base.
One-half the length of one side of the square base is (16/2) = 8 units.
Using the Pythagorean Theorem, we can write:
L^2 = (8^2) + (15^2)
L^2 = 64 + 225
L^2 = 289
Taking the square root of both sides, we find:
L = √289
L = 17
Therefore, the slant height of the square pyramid is 17 units.