This octagon is comprised of 8 isosceles triangles, each with two lateral sides of the length r and the angle of  = 45 degrees between them.

Very good.

Then the area of each of these triangles is half of the product r by itself and sin(45°)  
(see the lesson Formulas for area of a triangle in this site).

In other words, S1 =  =  = .

Now multiply it by 8, and you will get S =  for the area of the entire octagon.