Definition: A polygon that has one or more
interior angles greater than 180°

(Result: some vertices point 'inwards', towards the the center.)

(Result: some vertices point 'inwards', towards the the center.)

Try this
Adjust the polygon below by dragging any orange dot.
If any vertex points 'inward' to towards the interior of the polygon, it is a concave polygon.

A concave polygon is defined as a polygon with one or more interior angles greater than 180°. It looks sort of like a vertex has been 'pushed in' towards the inside of the polygon. Note that a triangle (3-gon) can never be concave.

A concave polygon is the opposite of a convex polygon. See Convex 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.

**Some of the**
diagonals
of a concave polygon will lie outside the polygon. In the figure on the right, the diagonal at the top of the polygon
is outside the polygon's interior space.
(In a
convex polygon,
all diagonals will lie inside the polygon).

**The area** of a concave polygon can be found by treating it as any other irregular polygon.
See Area of an Irregular Polygon

**Regular Polygons** are never concave by definition. See Regular Polygon Definition.

- Polygon general definition
- Quadrilateral
- Regular polygon
- Irregular polygon
- Convex polygons
- Concave polygons
- Polygon diagonals
- Polygon triangles
- Apothem of a regular polygon
- Polygon center
- Radius of a regular polygon
- Incircle of a regular polygon
- Incenter of a regular polygon
- Circumcircle of a polygon
- Parallelogram inscribed in a quadrilateral

- Square
- Diagonals of a square
- Rectangle
- Diagonals of a rectangle
- Golden rectangle
- Parallelogram
- Rhombus
- Trapezoid
- Trapezoid median
- Kite
- Inscribed (cyclic) quadrilateral

- Regular polygon area
- Irregular polygon area
- Rhombus area
- Kite area
- Rectangle area
- Area of a square
- Trapezoid area
- Parallelogram area

- Perimeter of a polygon (regular and irregular)
- Perimeter of a triangle
- Perimeter of a rectangle
- Perimeter of a square
- Perimeter of a parallelogram
- Perimeter of a rhombus
- Perimeter of a trapezoid
- Perimeter of a kite

- Exterior angles of a polygon
- Interior angles of a polygon
- Relationship of interior/exterior angles
- Polygon central angle

- Tetragon, 4 sides
- Pentagon, 5 sides
- Hexagon, 6 sides
- Heptagon, 7 sides
- Octagon, 8 sides
- Nonagon Enneagon, 9 sides
- Decagon, 10 sides
- Undecagon, 11 sides
- Dodecagon, 12 sides

(C) 2011 Copyright Math Open Reference.

All rights reserved

All rights reserved