Area of a concave quadrilateral

$\begingroup$

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.

$\endgroup$ 4

1 Answer

$\begingroup$

Having the lengths of the sides is not enough to calculate the area of a polygon (except triangle). But if you have the coordinates of the vertices then you are able to calculate the area. Here is how the formula looks like:

$\endgroup$ 1

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy