Question

Compute the exact value of the height

h of the square-based straight pyramid, given that the
base is a square with sides 28 centimeters long, and all other
edges are 34 centimeters long.

Answer 1

2√191 cm

Explanation:

You want the height of a right square pyramid with base edge lengths 28 cm and other edge lengths 34 cm.

Triangle

The lateral edge of the pyramid is the hypotenuse of a right triangle with one leg equal to the pyramid height, and the other leg equal to half the diagonal of the square. The diagonal of a square is √2 times the side length, so the relationship involved is ...

34² = h² + ((28√2)/2)²

1156 = h² +392

h² = 764

h = √764 = 2√191

The height of the pyramid is 2√191 cm.

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Additional comment

That's about 27.64 cm.

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