When calculating the lift coefficient, what area is used? Lets say I had this rectangular double curve wing. Orange represents the chord length, red represents the airfoil outline length below the chord line, green represents the airfoil outline length above the chord line, and blue represents the wing span. 

If I were to calculate its coefficient of lift, I would need to know the area. Which area does it refer to? Could you explain how to calculate the desired area using this diagram?

Could it be the length of green multiplied by the length of blue? Could it be the length of green and red multiplied by the length of blue? Or something else?

Correct me if I am wrong, but in this case, I think the planform area would be the length of orange multiplied by the length of blue.
Reference area for the aerodynamic coefficients (lift, drag, moment) is the planform area. Your picture shows only one wing, while the reference area S would also take into account the fuselage and the other wing: orange times twice blue and then some.

In its most generic case, the equation for wing area S is $$\int_{-b/2}^{b/2} c \cdot dy$$ with b = wing span = distance between the wing tips, c = local wing chord (orange line), y is the coordinate in direction $Y_m$.



For clarity in reference, the picture above from my old uni book by prof. Gerlach on stability &amp; control, which shows how the definition works when sweepback and dihedral angles must be accounted for. Note how the wing/fuselage intersection is defined for the reference wing area, by extending the local leading/trailing edges of the wings.