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. ![]() The name 'octagon' is derived from the Greek word 'oktágōnon' which means eight angles.The names of individual polygons are derived from the number of sides or corners the shape possesses. Octagon is an eight-sided two-dimensional geometrical figure which consists of 8 interior angles and 8 exterior angles. Then, after calculating the area of all the triangles, we add their areas to get the area of the octagon. We divide the octagon into smaller figures like triangles. In the case of an irregular octagon, there is no specific formula to find its area. It is expressed in square units like inches 2, cm 2, and so on. The area of an octagon is calculated with the formula, 2a 2(1 + √2) where 'a' is any one side length of the octagon. What is the Area of an Octagon With Side 5 units?Īrea of the octagon is 120.7 units 2. Where "a" denotes the length of the side of an octagon. The area of an octagon with side length a is 2a 2(1+√2). What is the Area of an Octagon with Side Length "a"? The area of an octagon with a radius of length r is 2√2r 2. What is the Area of an Octagon with a Radius? The area of an octagon with an apothem of length l is 8l 2(√2-1). ![]() What is the Area of an Octagon With an Apothem?Īpothem is the line segment drawn perpendicular to the side of the octagon from the center of the octagon. Where "s" denotes the length of the side of an octagon. Area of octagon formula = 2 × s 2 × (1+√2). ![]() To find the area of an octagon we use the following formula. If the shape is a polygon and it has eight sides, we call it an octagon. FAQs on Area of Octagon What is the General Formula of Area of Octagon?
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