I was asked a question by an engineering friend recently and was not certain of how to solve the problem. I know there are (somewhat complicated) formulae that compute the area of a quadrilateral (convex or concave) in terms of the sides and a diagonal or an angle, but is there a formula for the area of a concave quadrilateral in terms of just the side lengths?
My intuition is that the side lengths do not uniquely determine the quadrilateral, but I cannot prove this either. If the sides were specified by points on a coordinate system, I feel like the lengths would produce slopes, hence, angles, but I am not even certain this is true.
I have two questions: are the lengths of the sides enough to specify the quadrilateral? What is the area of the resulting figure? Any insight helps.