The Pyramid is an area in Memphis, Tennessee. Its height is 321 ft, and is slant height is 436.5 ft. Find the length of the edge of the square base. Round the answer to the nearest tenth.
We can use the Pythagorean theorem to solve this problem.
Let's label the height of the pyramid as "h", the slant height as "l", and the length of the edge of the square base as "s".
According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse (l) is equal to the sum of the squares of the other two sides (s and h). Therefore, we can set up the equation:
s^2 + h^2 = l^2
Squaring the measurements given:
321^2 + s^2 = 436.5^2
103,041 + s^2 = 190,561
Subtracting 103,041 from both sides:
s^2 = 87,520
Taking the square root of both sides to solve for s:
s ≈ √87,520
s ≈ 295.69
Therefore, the length of the edge of the square base is approximately 295.7 ft.