In this formula, n is equal to the number of sides of the polygon.Ī hexagon (six sides) can be divided into four triangles (6 - 2) and a dodecagon into 10 triangles (12 - 2).įor regular polygons, in which angles are all the same size and sides are the same length, the size of each angle in a polygon can be calculated by dividing the total size of angles (in degrees) by the total number of sides.įor a regular six-sided hexagon, each angle is: The above interior angle formula is derived by dividing a polygon into triangles, and this number can be found with the calculation:

(6 - 2) × 180° = 720° How Many Triangles in That Polygon? So the sum of the interior angles for a hexagon can be found by using the formula: Where n equals the number of sides of the polygon.

From a pentagon to a hexagon (five to six sides)Īnother 180° is added to the total of the interior angles.

From a triangle to quadrilateral (three to four sides).

A star-shaped hexagram is a six-sided, complex polygon created by overlapping two equilateral triangles.Īs a rule, each time a side is added to a polygon, such as:.

A regular-shaped hexagon is a six-sided, simple polygon.

The names of complex polygons are sometimes different from those of simple polygons with the same number of sides.

Complex polygons: The lines intersect more than once.

Simple polygons: The lines connect or intersect only once - at the vertices.

Concave polygons: Have at least one internal angle that is greater than 180°.Īnother way to classify polygons is the way the lines forming the polygon intersect.

Convex polygons : Have no internal angles greater than 180°.

Irregular polygon: Does not have equal-sized angles or sides of equal length.Ī second way to classify polygons is by the size of their internal angles.

Regular polygon: All of the angles are of equal size, and all the sides are equal in length.

Polygons are classified based on whether or not all angles or sides are equal. However, in mathematics, pentagons are sometimes more conveniently referred to as n-gons: So, a 100-sided polygon is referred to as a hectogon. Polygons with more than 10 sides are encountered infrequently but follow the same Greek naming convention.

Square: Sometimes, a four-sided polygon (a square) is referred to as a quadrangle or tetragon.

Quadrilateral: Derived from the Latin prefix quadri, meaning four, attached to the word lateral, which is another Latin word meaning side.

Trigon is the correct geometrical name but is rarely used.

Triangle: Uses the Greek prefix Tri, but instead of the Greek gon , the Latin angle is used.

Most notably with words more commonly used for some polygons: There are exceptions to this naming scheme.

Hexa (Greek meaning six) + gon = hexagon.

Penta (Greek meaning five) + gon = pentagon.

The common name for most polygons is the Greek prefix for 'sides' attached to the Greek word for corner (gon).Įxamples of this for five and six-sided regular polygons are: Polygons have the same number of sides and corners. department of defense building in Washington D.The names of individual polygons are derived from the number of sides or corners the shape possesses. Thus all concave pentagons are irregular.

Concave Pentagon: Have at least one vertex pointing inwards whose angle is greater than 180°.

Convex Pentagon: Have all vertices pointing outwards and thus the angles formed are less than 180°.Irregular Pentagon: Does not have all sides equal or all angles equal and thus have no specific angles.A regular pentagon has five lines of symmetry. Drawing diagonal lines between the nonadjacent vertices of a regular pentagon results in a star shape known as pentagram. A regular pentagon are thus both equilateral (having five equal sides) and equiangular (having five angles of equal measure). Regular Pentagon: Have five sides of equal length and five interior angles each measuring 108° and exterior angles of 72°each.Area ( A) = 5/2( s x a), here s = 6 cm and a = 8 cmĭepending on the sides, angles, and vertices, pentagon shapes are classified into the following types:

Different shapes of pentagon