Regular Octogan

When I was at a hotel recently, I noticed that the table was a regular octagon. Because this picture was taken at a distance, the table is distorted. From straight on top the table would look more like this.

I wanted to find the area of the octagon.  The equation for this is (1/2)(apothem)(perimeter).  The apothem is the length from the center to the midpoint of one of the sides.

Here, segment OI is the apothem and is 4.35 cm.  Each side is 3.61 cm. The real table's sides were about 0.6m or 60cm. To find the real apothem we can set up a proportion with
                                                                               

                           







This equals 72.299cm, the length of the apothem.  Then, we can find the area of the octogon

(~NW5)