We can do this the easy way or the hard way.
The hard way involves setting up and solving a series of equations involving a,b,s and r in the above figure. And then noting that the area of the octagon is (2r)^2-2ab.
The easy way is to note that by drawing lines from each vertex to the centre, the octagon can be dissected into eight triangles, each of base s and height r. So the area is simply 4rs, which given s=17 and r=19 gives an area of 1292.
I recently used the fact that there are two ways to calculate the area to provide a proof of Pythagoras Theorem.
