Question

use the image to answer the question.
321 ft.
436.5 ft.
$l$
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)
$square$ ft.

Explanation:

Step1: Find half the base edge length

Let $x$ be half the length of the square base edge. Use the Pythagorean theorem with height $h=321$ ft and slant height $l_s=436.5$ ft:
$$x = \sqrt{436.5^2 - 321^2}$$
$$x = \sqrt{190532.25 - 103041}$$
$$x = \sqrt{87491.25} \approx 295.789$$

Step2: Find full base edge length

Multiply $x$ by 2 to get the full edge length $l$:
$$l = 2 \times 295.789$$

Answer:

591.6 ft