The central angle is 

The SAS formula for the area of a triangle is

"The area of a triangle is equal to one-half the product of
two sides multipled by the sine of the included angle.

Area of the triangle = 

and as we see below:



the regular octagon is composed of 8 such triangles,
all congruent.  Therefore:

The area of the regular octagon = .

That's approximately 282.8427125 square units.

Edwin