Question

A square pyramid is shown. Its height is shown with a dotted line labeled 321 feet. Its slant height is shown with a dotted line labeled 436.5 feet. The variable l is shown along one of the edges of the square base.
The Pyramid is an arena in Memphis, Tennessee. Its height is 321 ft., and its slant height is 436.5 ft. Find the length of the edge of the square base. Round the answer to the nearest tenth.

Answer 1

Let the base edge be l. The slant height s, height h, and half the base form a right triangle:
s^2 = h^2 + (l/2)^2.

So
(l/2)^2 = s^2 − h^2
l = 2√(s^2 − h^2).

With s = 436.5 and h = 321:
s^2 − h^2 = 436.5^2 − 321^2 = 190,532.25 − 103,041 = 87,491.25,
√(87,491.25) ≈ 295.789,
l ≈ 2(295.789) ≈ 591.578.

Rounded to the nearest tenth: 591.6 ft.