Find the maximum possible area of a convex quadrilateral having sides of lengths 1, 4, 7 and 8.

Side order is completely irrelevant.

Draw in a diagonal.  Reflect one of the two resulting triangles about the perpendicular bisector of the diagonal.

You haven't changed the area, just the order of the sides.  So the maximum area of any order is the same.

Posted by Jer on 2016-07-03 22:10:49