Results for this submission At least one of the answers above is NOT correct. The diagonals of a convex quadrilateral are mutually perpendicular. The sum of the lengths of the diagonals is 12. We want to find the maximum possible area of such a quadrilateral. Let us denote b :2: and _ the lengths of the two diagonals. Then the area of the quadrilateral is the following function of x and y: (1/2)XV If we solve for in terms of at, we can reexpress this area as the following function of a: alone: 12-x Thus we nd that the maximum area is 18