Type the correct answer in the box. Use numerals instead of words. A right square pyramid has an altitude...

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Type the correct answer in the box. Use numerals instead of words.
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?
x = _____ units

SnapAndSolve AI · Accepted Answer

To find the distance from the apex to each vertex of the base, we can use the Pythagorean theorem in two steps:

First, find the distance from the center of the base to a vertex of the base. Since the base is a square with side length 6, the distance from the center to a vertex is half the diagonal of the square. The diagonal of the square is given by:
Diagonal = √(6² + 6²) = √72 = 6√2
Half of this diagonal is: 3√2
Now, use the Pythagorean theorem to find the distance from the apex to a vertex of the base. The apex, the center of the base, and a vertex of the base form a right triangle with the altitude as one leg (10), the half-diagonal as the other leg (3√2), and the hypotenuse as the distance we need to find (x):
x = √(10² + (3√2)²) = √(100 + 18) = √118 ≈ 10.9

Therefore, x = 10.9 units.

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Type the correct answer in the box. Use numerals instead of words. A right square pyramid has an altitude...

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