John M. answered • 03/25/18

Tutor

New to Wyzant
High School and College Science Tutor

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**