Question

Given quadrilateral ABCD. M, N are the midpoints of BC, AD. Set: AC=x, BD=y, MN=z, and \(p=\frac{x+y+2z}{2}\). Prove that: \(S_{ABCD}=\sqrt{p\left(p-x\right)\left(p-y\right)\left(p-2z\right)}\)