Question

Could anyone help me understand this problem?

Answer 1

It seems you will have to use a LOT of trigonometric calculations.
Line AC = 26 
Line AD = 13 = Line DC = 13
Line BF = 13

Angle ABC = Angle GBF = Angle FBH = 55 degrees each

cosine 40 = 13 (Line AD) / Line AE  
Line AE = 13 / 0.76604  = 16.97

tangent 40 = ED / AD = ED / 13
Line ED = 0.8391 * 13 = 10.908

Line DC =13
 
Angle ABC = 55 degrees
tangent(55) = 26 / AB
AB = 26 / 1.4281  = 18.206

Well, that's about half the calculations.
(As I said it's a lot of work).