ABX is a triangle. AMX is a right triangle. AM is one-half of AB, so it is 4. The measure of the angles in an octagon will add up to 180(8-2) which is 1080°, so each angle would be 135°, and angle XAM would be half of that, so 67.5°.
tan 67.5 = XM/4
4(tan 67.5) = XM
XM = 9.66
XC is the same as XA, so
cos 67.5 = 4/XC
XC = 4/cos 67.5
XC = 10.45
The octagon ABCDEFGH can be divided into 8 identical triangles all congruent to ABX, so the area would be
A = 8(1/2)bh
A = 8(1/2)(8)(9.66)
A = 309.12
