Answer:
321.1 ft
Step-by-step explanation:
Linear Distance
Let's imagine a square-based pyramid of side L and height H. Please refer to the image provided below where a simplified drawing of the pyramid shows the diagonal distance D that the marble has to travel to reach the base of the pyramid from the very top of it, assuming it rolls by the very center of one of the sides.
The distance can be calculated by
[tex]\displaystyle D=\sqrt{\left(\frac{L}{2} \right)^2+H^2}[/tex]
We need to find the length of the side of the square base. We know its area is [tex]349,281 ft^2[/tex]. The area of a square is
[tex]A_s=L^2[/tex]
We solve for L
[tex]L=\sqrt{A}=\sqrt{349,281 }=18.9\ ft[/tex]
Now we compute D
[tex]\displaystyle D=\sqrt{\left(\frac{18.9}{2} \right)^2+321^2}[/tex]
[tex]\boxed{D=321.1\ ft}[/tex]
