Hunter's Woods PH

Montessori Geometry

Convex vs. Concave Polygons

Learn the difference between convex and concave polygons and use the free worksheets to help reinforce learning.

What are convex and concave polygons?

Polygons are either convex or concave. A polygon is convex if each of its interior angles measures less than 180°; otherwise it is concave. They are sometimes called convex and concave shapes — polygons are shapes that are closed, two-dimensional, and made of straight (not curved) lines.

Convex vs. concave quadrilaterals

Quadrilaterals are simply polygons with four sides, thus the same definitions apply. A convex quadrilateral is a four-sided polygon whose interior angles all measure less than 180°. A four-sided polygon that has an interior angle over 180° is considered a concave quadrilateral.

Are all regular polygons convex?

A regular polygon is a polygon that is equilateral (all sides have the same length) and equiangular (all angles are equal in measure). Since the angles of regular polygons have to be equal, it is impossible for them to be over 180° — for that reason, all regular polygons are convex. 

  • There is a shape called a regular star polygon that is said to be non-convex, but it rather distorts the definition of a regular polygon.

Convex vs. Concave Polygons: Worksheet 1

Convex vs. Concave Polygons: Worksheet 2

Did you enjoy this worksheet on convex vs. concave polygons?

Answer these Math and Geometry worksheets next!

Check out the Montessori-inspired resources available here for free.