# Given the sides of a polygon, determine if it is convex or concave

We are given the lengths of all sides of a polygon. We need to determine if the given polygon is convex or concave. How can this be done? What is the propery applied to determine this?

• Dec 6, 2015 at 19:02
• ohkk.. thanx a lot . In case if we are given some straight lines (with length of each of them) , how can we determine if convex polygon formation is possible or not using each of those lines? Dec 6, 2015 at 19:05
• @user249117 If it's possible to form a polygon from given line segments, then it's possible to form a convex one from these. Dec 6, 2015 at 19:15
• @Wojowu thanks a lot :) Dec 6, 2015 at 19:18
• What is a "concave polygon", by the way?
– user147263
Dec 6, 2015 at 20:14

Additional remark: if you know the coordinates $V_j$ of vertices, then the signs of scalar cross-products of vectors $V_jV_{j+1}$ can be used to determine convexity. I.e., the determinants such as $$\begin{vmatrix} V_2^x-V_1^x & V_3^x-V_2^x \\ V_2^y-V_1^y & V_3^y-V_2^y \end{vmatrix}$$ must be all $\ge 0$, or all $\le 0$. (Including one with $V_n$ and $V_1$ to close the loop.)