Approximate Method $-$ Trusses $(25$ points$)$:

The diagonals of the truss are to be designed to support both tensile and compressive forces $($hint$.$ half and half$).$ Assume $A$ is a pin and $C$ is a roller. An external force $20kN$ is applied at $B,$ and thus the corresponding support reactions are solved as $A_y=10kN$ and $C_y=10kN.$

$(1)$ Solve for the forces in the members $FB$ and $AE$;

$(2)$ Solve for the forces in the members $FE,AF,$ and $AB.$