DE-MO 1999 Problem 3

A mathematician investigates methods of finding area of a convex quadrilateral obtains the following formula for the area $A$ of a quadrilateral with consecutive sides $a,b,c,d$ : $A =\frac{a+c}{2}\frac{b+d}{2}$ (1) and $A = \sqrt{(p-a)(p-b)(p-c)(p-d)}$ (2) where $p = (a+b+c+d)/2$ . However, these formulas are not valid for all convex quadrilaterals. Prove that (1) holds if and only if the quadrilateral is a rectangle, while (2) holds if and only if the quadrilateral is cyclic.