Question

PLEASEE HELP 20 POINTS Find the area of an octagon with a radius of 6 meters. Round your answer to the nearest tenth.

Answer 1

ok, I'm not sure since this is the answer, because I had someone else do it for me, but I got 184,905 as my answer, so I guess the area would be 184, 910 if rounded. As I said before, not too sure.

Answer 2

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