A right square pyramid has an altitude of 10 and each side of the base is 6. To the nearest tenth of a centimeter, what is the distance from the apex, or top of the pyramid, to each vertex of the base?
Right square pyramid is represented. The square base has side labeled 6. The height of the pyramid is labeled 10. Edge along the top vertex of a triangular face is labeled x.
We can use the Pythagorean Theorem to find the distance from the apex to each vertex of the base.
If we draw a vertical line connecting the apex to the center of the base, we form a right triangle. The height of the pyramid is the hypotenuse of this triangle, and the distance we want to find is one of the legs.
Using the Pythagorean Theorem, we have:
x^2 + (6/2)^2 = 10^2
Simplifying, we have:
x^2 + 9 = 100
Subtracting 9 from both sides, we have:
x^2 = 91
Taking the square root of both sides, we have:
x ≈ 9.5
Therefore, to the nearest tenth of a centimeter, the distance from the apex to each vertex of the base is approximately 9.5 cm.