How do you know if a polygon is convex or concave?
Every polygon is either convex or concave. The difference between convex and concave polygons lies in the measures of their angles. For a polygon to be convex, all of its interior angles must be less than 180 degrees. Otherwise, the polygon is concave.
A concave polygon is a polygon that is not convex. A simple polygon is concave iff at least one of its internal angles is greater than . An example of a non-simple (self-intersecting) polygon is a star polygon. A concave polygon must have at least four sides.
- Concave or Convex. A convex hexagon has no angles pointing inwards. More precisely, no internal angles can be more than 180°.
- The simplest polygon is a triangle (a 3-sided shape). Polygons of all types can be regular or irregular. A regular polygon has sides of equal length, and all its interior angles are of equal size. Irregular polygons can have sides of any length and angles of any size. In fact, they are the only polygons which do.
- In Euclidean geometry, an equiangular polygon is a polygon whose vertex angles are equal. If the lengths of the sides are also equal (that is, if it is also equilateral) then it is a regular polygon. Isogonal polygons are equiangular polygons which alternate two edge lengths.
A polygon is a closed shape with straight sides. A concave polygon is one that has at least one angle larger than 180 degrees, causing the polygon to 'gape open' at the corners where whose angles occur. A convex polygon is one whose angles are all smaller than 180 degrees.
- The interiors of circles and of all regular polygons are convex, but a circle itself is not because every segment joining two points on the circle contains points that are not on the circle. A set in a space that is not convex is called a concave set.
- The sum of the exterior angles of any convex polygon is 360 degrees. That means that if you have n sides, then each exterior angle of a regular polygon is 360/n. If you can find out how the exterior angle is related to the interior angle, you can finish the solution.
- The sum of the interior angles in a regular polygon is given by the formula 180(n – 2), where n is the number of sides in the polygon. An octagon has eight sides, so the sum of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 degrees.
Updated: 3rd December 2019