A dodecagon is a polygon with 12 sides and also 12 vertices. "Do-" means "two" and "deca-" way "ten."

Dodecagon classifications

Like various other polygons, a dodecagon can be divide as constant or irregular.

You are watching: Number of diagonals in a dodecagon

Regular dodecagonIrregular dodecagon
*
*
All sides and also interior angles are congruentSides and angles have actually various lengths

A dodecagon can likewise be classified as convex or concave.

A convex dodecagon is a polygon wherein no heat segment between any kind of two points on its boundary lies external of it. Nobody of the inner angles is greater than 180°. Think the a convex dodecagon together bulging outwards, such as the constant dodecagon pictured above.

Conversely, a concave dodecagon, like the rarely often, rarely dodecagon displayed above, has at least one line segment that have the right to be drawn between points top top its boundary but lies external of it. Also, at the very least one the its inner angles is greater than 180°.

A convex dodecagon go not need to be a regular dodecagon. Yet, a regular dodecagon is constantly a convex dodecagon. The dodecagon listed below is convex but clearly has sides and also angles that room not congruent. This dodecagon is irregular.

*

Angles that a dodecagon

Dodecagons can be damaged into a series of triangle by diagonals drawn from its vertices. This collection of triangles have the right to be offered to find the amount of the internal angles of the dodecagon.

Diagonals are drawn from peak A in the convex dodecagon below, forming 10 triangles. Similarly, 10 triangle can additionally be attracted in a concave dodecagon. Because the sum of the degrees in a triangle is 180°, the sum of the interior angles the a dodecagon is 10 × 180° = 1800°.

See more: How Many Nanometers Are In A Centimeter To Nanometer Conversion (Cm To Nm)

*

A consistent dodecagon has actually equal internal angle measures. Since 1800°/12 = 150°, each interior angle in a continuous dodecagon has actually a measure of 150°. Also, every exterior angle has a measure up of 30° since the exterior angle and also interior angle kind a straight angle.