An octagon is a polygon that has actually eight sides. In the figure below are 3 different species of octagons. A prevent sign is an instance of objects in everyday life the is in the shape of an octagon.

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Octagon classifications

Like other polygons, one octagon can be share as continual or irregular. If all the sides and interior angles of one octagon room equal, it is a constant octagon. Otherwise it is an irregular octagon.

Regular octagonIrregular octagon
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All sides and also interior angles room equalNot every sides and also angles space equal

Octagons and other polygon can also be classified as either convex or concave. If all inner angles of an octagon or polygon are less than 180°, the is convex. If one or an ext interior angle are bigger than 180°, it is concave. A constant octagon is constantly a convex octagon.

Convex octagonConcave octagon
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All internal angles 180°

Parts of one octagon

Diagonals of one octagon

A diagonal line is a heat segment joining two non-consecutive vertices. Five diagonals have the right to be drawn from every vertex. A full of 20 diagonals deserve to be drawn for one octagon. The following figure is an example.

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Internal angles of an octagon

The sum of the internal angles of an octagon equates to 1080°.

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As presented in the figure above, 5 diagonals have the right to be drawn to divide the octagon right into six triangles. The blue lines over show just one way to divide the octagon right into triangles; there room others. The amount of internal angles the the 6 triangles amounts to the sum of interior angles of the octagon. Because the sum of the interior angles that a triangle is 180°, the amount of the interior angles because that the hexagon is 6 × 180° = 1080°.

Regular octagons

A continual octagon is one octagon whose sides space equal in length, and whose internal angles are equal in measure.

Since every of the eight inner angles in a regular octagon are equal in measure, each internal angle procedures 1080°/8=135° as shown below.
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Each exterior angle for a continuous octagon has an same measure. The exterior angles of a constant octagon have an edge of 45°.
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Symmetry in constant octagons

A constant octagon has actually 8 lines of symmetry and also a rotational the opposite of order 8. This means that it have the right to be rotated in such a method that it will look the very same as the initial shape 8 time in 360°.

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Lines of symmetryRotational symmetry
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8 lines of symmetryEight 45°angles of rotation

Area the a constant octagon

The area that a continual octagon with side size s is:

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. Accordingly, the side length of the square is
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. The area of the octagon have the right to be calculated by individually the locations of the four right triangles from the area the the square.