area of a regular polygon (octagon) with an apothem of 4.5

There are several ways to do this.......let's find 1/2 of a side length of the octagon

We have

(1/2)s/sin22.5 = 4.5/ sin 67.5

(1/2)s = [4.5 sin 22.5] / sin67.5 = about 1.864

So we have 8 triangles with heights of 4.5 and a side length of about 3.728

So, the area is given by

8 * (1/2) *3.728 * 4.5  = about 67.1 sq units