1. The problem involves a hexagon with vertices A, B, C, D, E, F and edges AB, BC, CD, DE, BF, AF. 2. Given lengths: AB = BC = a, EF = DE = a, AF = 3W. 3. The angle between AB and BC is given by the magnitude \( \sqrt{3}a \). 4. Similarly, angle between EF and DE is 60 degrees and their magnitude is \( \sqrt{3}a \). 5. The problem states the relationship involving AF and AB with the factor 3W and coefficient 0.5 affecting measurements. 6. For the force diagram: at point C, force of 300 N acts horizontally. 7. To find the relationship between AF and AB, observe that:\n AF = 3W, AB = a, with a proportional factor 3 at point A. 8. Using vector form, considering hexagon geometry and angles of 60 degrees, one can conclude the relationships in forces and lengths reaffirming AF = 3W and AB = a with the given angles. 9. Therefore, the relationship between AF and AB is maintained as AF = 3 times AB times W (where W is a scaling factor). Final answer: \n$$ AF = 3 W \times AB = 3 W a $$ This matches the problem's description and confirms the relationship between the sides and forces in the hexagon and force diagram given.