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 6 square root of 3 in., 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. Find the length (in inches) of the altitude of the pyramid.

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