Definition: A polygon that has all
interior angles less than 180°

(Result: All the vertices point 'outwards', away from the center.)

(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.

**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.

- 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
- Trapezium
- 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

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