The next logical step would have been to drawn lines extending from the sides of all the triangles to the property line of the sight. This would set the boundaries for the eventual ellipse shape. The architect would have then specified the dimensions for the arena floor, and drawn two points on the plan on each vertex, which he would connect with an elliptical arc. This would be the shape and outline of the arena floor. To get the outside walls, he or she would simply have to repeat the procedure over and over, each time offsetting the arcs until he got to the desired width. The final building came out to be 620'-4" long and 511'-9" wide at the origin, with walls rising 158' from the ground level. .
The site for the Colosseum was also, as was everything, carefully planned out. After the previous emperor Nero died, his "Domus Aurea" (Golden Temple) still remained on the site. Vespasian, not particularly wanting the palace to stick around decided to destroy the entire site and use it for his "gift" to the public. The problem with the site was that it was situated on the shores of a spring fed lake (Nero's lake) and at certain times during the year it would turn the whole site into a wetland. To make the issue even worse, the Colosseum would sit partially on top of the lake. To solve the issue of the site becoming a wetland, and to prevent the Colosseum from flooding and its foundation weakening each time the lake flooded, the drainage and foundation of the building were engineered to perfection. Rather than building walls around the lake, the engineers designed the foundation to sit on the clay bed of the lake, nearly 25' below the ground level with drains built under the entire circumference of the foundation, as well as drains throughout the entire area inside the Colosseum spaced every 12'. The drains led to pipes and eventually into the storm drain system that Rome was famous for.