In a convex pentagon ABCDE, let \angle EAB \equal{} \angle ABC \equal{} 120^{\circ}, \angle ADB \equal{} 30^{\circ} and \angle CDE \equal{} 60^{\circ}. Let AB \equal{} 1. Prove that the area of the pentagon is less than 3. geometrytrigonometryinequalitiescyclic quadrilateralgeometry proposed