find the are of a regular octagon whose sides are 12cm long.

Answer 1

cut the octogon into 8 congruent triangles, with vertices at the centre of the octogon.

Consider one of those triangles.
It will have a base of 12 cm, and the angle across from the 12 will be 45º, with the other two angles 67.5º each.
Let its height be h.
tan 67.5 = h/6
h = 14.485

so the area of that triangle is 1/2(12)(14.485
= 86.912

so the octogon is 8(86.912) = 695.29 cm^2