The pyramid is an arena in Memphis Tennessee. Its height is 321 feet and it slant height is 436.5 feet find the length of the edge of a square base.
To find the length of the edge of the square base of the pyramid, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the other two sides.
Let's label the length of the edge of the square base as x.
Using the Pythagorean theorem, we have:
x^2 + x^2 = 436.5^2
Simplifying the equation, we get:
2x^2 = 436.5^2
Dividing both sides by 2, we get:
x^2 = (436.5^2)/2
Taking the square root of both sides, we get:
x = √((436.5^2)/2)
Calculating this on a calculator, we find:
x ≈ 309.8 feet
Therefore, the length of the edge of the square base of the pyramid is approximately 309.8 feet.