A regular octagon can be thought of as being composed of 4 "kite" shaped areas.
The area of a "kite" with diagonals d and w is
AreaKITE=d⋅w2.
(This is fairly easy to prove if it isn't a formula you already know).
Consider the "kite" PQCW in the diagram above.
∠QCW=π2 and |QC|=|WC|=r
s⇒|QW|=√2r (Pythagorean)
Therefore (since |PC|=r)
AreaPQCW=|PC|⋅|QW|2=r⋅√2r2=√2r^22
The octagon is composed of 4 such kites, so
AreaOctagon=2√2r^2
AreaOctogon=2√2(6)^2=101.823376491
AreaOctagon=101.8 units squared
here is the diagram https://d2gne97vdumgn3.cloudfront.net/api/file/80fl6nYTCaa5q8AZOyq0
