Through the diagonals and the angle between them

The second method is based on the diagonals of a parallelogram and the angle between them. Proof: Diagonals divide a parallelogram into 4 triangles, respectively, the parallelogram area will consist of the areas of these triangles: Using the formula to find the area of the triangle and taking into account that sin (α) = sin (180⁰ - α), then one and all triangles will have one and the same sin (α), because between the diagonals all the angles are complementary to each other up to 180 °. Thus, we obtain the above formula for any parallelogram.