Question 846939
<pre>
Each central angle is {{{"360°"/8="45°"}}}

{{{drawing(400,400,-1.5,1.5,-1.5,1.5,

line(1,0,0.70710678,0.70710678),
line(0.70710678,0.70710678,0,1),
line(0,1,-0.70710678,0.70710678),
line(-0.70710678,0.70710678,-1,0),
line(-1,0,-0.70710678,-0.70710678),
line(-0.70710678,-0.70710678,0,-1),
line(0,-1,0.70710678,-0.70710678),
line(0.70710678,-0.70710678,1,0),

line(1,0,0,0),
line(0.70710678,0.70710678,0,0),
line(0,1,0,0),
line(-0.70710678,0.70710678,0,0),
line(-1,0,0,0),
line(-0.70710678,-0.70710678,0,0),
line(0,-1,0,0),
line(0.70710678,-0.70710678,0,0),
locate(.3,-.9,4m),locate(.02,-.19,"45°"),
green(line(.3535533906,-.8535533906,0,0)),
locate(.11,-.8,2m), green(locate(.25,-.4,h))

 )}}}


The green line bisects the isosceles triangle,
so the angle at the top is 22.5° and the base
of the right triangle is 2m, so

tan(22.5°) = {{{2/h}}}

h*tan(22.5°) = 2

h = {{{2/tan("22.5°")}}} = 4.828427125

So the area of the whole triangle is 

A = {{{1/2}}}*b*h = {{{1/2}}}*4*4.828427125 = 9.656854249

The area of the whole octagon is 8 times that or

9.656854249×8 = 77.254834

Incidentally h is called the "apothem".

Edwin</pre>