Concave polygon


A concave polygon is one that has at least one of its angles that is greater than 180º. Thus, at least one of its diagonals is outside the figure.

It should be noted that a concave polygon can be decomposed into other figures, for example, triangles.

In addition, it is worth mentioning that the triangle is the only polygon that cannot be concave because none of its interior angles can be greater than 180º.

Elements of a concave polygon

The elements of a concave polygon are:

  • Vertices: They are the points whose union forms the sides of the figure. In the image below, vertices would be A, B, C, and D.
  • Sides: They are the segments that join the vertices form the polygon. In the figure they would be AB, BC, CD and AD.
  • Internal angles: Arch that is formed from the union of the sides. In the example below they would be: α, β, δ, γ.
  • Incoming angle: It is the interior angle greater than 180º. In the example shown, it would be the angle δ. It should be noted that a concave polygon with n sides, the maximum number of concave angles will be n / 2.
  • Diagonals: They are the segments that join each vertex with some non-continuous vertex. In the figure below, the diagonal AC is exterior, which shows that it is a concave polygon. Meanwhile, the diagonal BD is interior.
Concave polygon Other

Examples of concave polygons

Some examples of concave polygons are stars like the following:

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