Question

use the image to answer the question.
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.
(1 point)

Explanation:

Step1: Use the Pythagorean theorem for the right - triangle formed

Let \(x\) be half of the side length of the square base. In the right - triangle with height \(h = 321\) ft and slant height \(l_s=436.5\) ft, by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 436.5\) (slant height) and \(a = 321\) (height), and \(b=x\).

$$x=\sqrt{436.5^{2}-321^{2}}$$

First, calculate \(436.5^{2}=436.5\times436.5 = 190532.25\) and \(321^{2}=321\times321=103041\).
Then \(x=\sqrt{190532.25 - 103041}=\sqrt{87491.25}\approx295.8\)

Step2: Find the side length of the square base

Since \(x\) is half of the side length of the square base, if the side length of the square base is \(s\), then \(s = 2x\).
\(s=2\times295.8 = 591.6\)

Answer:

\(591.6\) ft