To find the length of the edge of the square base of the pyramid, we can use the Pythagorean theorem. The slant height of the pyramid is the hypotenuse of a right triangle formed by the height and half of the length of the base.
Let's call the length of the base l.
Using the Pythagorean theorem, we can write:
l^2 + (l/2)^2 = 436.5^2
Simplifying the equation:
l^2 + l^2/4 = 191000.25
Multiplying both sides by 4 to eliminate the fraction:
4l^2 + l^2 = 764001
Combining like terms:
5l^2 = 764001
Dividing both sides by 5:
l^2 = 152800.2
Taking the square root of both sides:
l ≈ √152800.2
l ≈ 390.6
Therefore, the length of the edge of the square base of the pyramid is approximately 390.6 feet (rounded to the nearest tenth).
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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