To find the length of the edge of the square base, we can use the Pythagorean theorem.
Let l be the length of each edge of the square base. The Pythagorean theorem states that the square of the slant height is equal to the sum of the squares of the height and half the length of the base:
l^2 + l^2 = 436.5^2 - 321^2
2l^2 = 190282.25 - 103041
2l^2 = 87241.25
l^2 = 43620.625
l = sqrt(43620.625)
l ≈ 208.8 ft
Therefore, the length of the edge of the square base is approximately 208.8 feet.
Use the image to answer the 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.
(1 point)
ft.
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