What Is a Concave Quadrilateral?

concave-quadrilateral Credit: fdecomite/CC-BY 2.0

A concave quadrilateral is a shape that has four sides and contains an indentation where the internal angle is greater than 180 degrees. The most common example of a concave quadrilateral is a shape whose left and right sides resemble a triangle; however, instead of meeting in a straight line as a base, they meet at another vertex angled towards their upper vertex.

The definition of concave is curved inwards. When applied to polygons, this means that the shape must have some sort of dent in it (at least one vertex pointing inwards). The definition of a quadrilateral is a two-dimensional figure that has four sides. Therefore, a concave quadrilateral must satisfy both of these definitions. Furthermore, a concave quadrilateral must also satisfy the definition of a simple shape. A shape that is not simple intersects with itself. A concave quadrilateral is simple, then, by the fact that it does not intersect with itself at any point.

A more accurate definition of a quadrilateral is a polygon whose internal angles add up to 360 degrees. In a square, for example, four 90-degree angles are added together for 360 degrees. Since a concave polygon has one angle measuring greater than 180 degrees, the sum of its three other angles must be 180.