What is the formula for area projection of dihedral angles?

I drew it in a cube. In the picture, the triangle HGF is the projected area of ??the triangle CHF on the base. Therefore, according to S projection = S oblique multiplied by cosθ, that is, S angle HGF = S triangle CHF multiplied by cosθ. The triangle HGF and the triangle CHF can be calculated and then we can get cosθ. I hope you will give me points and don’t let me draw the picture for a long time in vain. I hope you can understand it and apply it skillfully