Convex Polygon

Definition: A polygon that has all interior angles less than 180°
(Result: All the vertices point 'outwards', away from the center.)
Try this Adjust the polygon below by dragging any orange dot. If any vertex points 'inward' to towards the center of the polygon, it ceases to be a convex polygon.

A convex polygon is defined as a polygon with all its interior angles less than 180°. This means that all the vertices of the polygon will point outwards, away from the interior of the shape. Think of it as a 'bulging' polygon. Note that a triangle (3-gon) is always convex.

A convex polygon is the opposite of a concave polygon. See Concave Polygon.

In the figure above, drag any of the vertices around with the mouse. Take note of what it takes to make the polygon either convex or concave. Also change the number of sides.

Properties of a Convex Polygon

A line drawn through a convex polygon will intersect the polygon exactly twice, as can be seen from the figure on the left. You can also see that the line will divide the polygon into exactly two pieces.

All the diagonals of a convex polygon lie entirely inside the polygon. See figure on the left. (In a concave polygon, some diagonals will lie outside the polygon).

The area of an irregular convex polygon can be found by dividing it into triangles and summing the triangle's areas. See Area of an Irregular Polygon

Regular Polygons are always convex by definition. See Regular Polygon Definition. In the figure at the top of the page, click on "make regular" to force the polygon to always be a regular polygon. You will see then that, no matter what you do, it will remain convex.

Other polygon topics


Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons