The regular octagon can be divided into 8 congruent isosceles triangle
so
The area of the regular octagon is the same that the area of 8 congruent isosceles triangles
so
See one isosceles triangle in the figure below
Find out the height of the triangle
tan(67.5)=h/2.5
h=2.5*tan(67.5)
the area of the regular octagon is equal to
A=8*(1/2)*[5*2.5*tan(67.5)]
A=120.7 cm2
