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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)

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Answer 1

To find the length of the edge of the square base of the pyramid, you can use the Pythagorean theorem.

The formula is: l^2 + h^2 = s^2, where l is the length of the edge of the square base, h is the height, and s is the slant height.

In this case, we know that h = 321 ft. and s = 436.5 ft.

Substituting these values into the formula:

l^2 + (321 ft.)^2 = (436.5 ft.)^2

l^2 + 103,041 ft.^2 = 190,522.25 ft.^2

l^2 = 190,522.25 ft.^2 - 103,041 ft.^2

l^2 = 87,481.25 ft.^2

To find l, take the square root of both sides:

l = √(87,481.25 ft.^2)

l ≈ 295.9 ft.

Therefore, the length of the edge of the square base is approximately 295.9 feet.