In a regular pyramid, the lengths of the apothem a of the base, the altitude h, and the slant height ℓ satisfy the Pythagorean Theorem; that is, ℓ2 = a2 + h2.

Question

Use the following theorem to answer the question.

In a regular pyramid, the lengths of the apothem a of the base, the altitude h, and the slant height ℓ satisfy the Pythagorean Theorem; that is, ℓ² = a² + h².

In a regular hexagonal pyramid whose base edges measure 63  the apothem of the base measures 9 in. The slant height of the pyramid is 15 in. If the length of the altitude h is to be found using the formula in the theorem, determine the values (in inches) of the variables ℓ and a.

PLEASE SHOW ME THE STEPS

ℓ=  

a=

Find the length (in inches) of the altitude of the pyramid.

Answer 1

α, the apothem is given as 9 in.

h² + 9² = 15²