The pyramid is in arena in Memphis Tennessee. It’s height is 321 feet and it’s slant height is 436.5 feet find the length of the edge of the square base around the answer to the nearest 10th.

Answer 1

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

Let's call the length of the edge of the square base "x". We can form a right triangle by connecting the height, the slant height, and half of the base diagonal (which is equal to half the length of the edge of the square base).

According to the Pythagorean theorem, the square of the length of the height plus the square of half the base diagonal should equal the square of the slant height.

So, we have:

height^2 + (half the base diagonal)^2 = slant height^2

321^2 + (x/2)^2 = 436.5^2

103041 + (x^2/4) = 190693.25

x^2/4 = 87552.25

x^2 = 350209

x ≈ √350209 ≈ 591.7

Therefore, the length of the edge of the square base, rounded to the nearest tenth, is approximately 591.7 feet.