An octagon is a polygon that has eight sides. In the figure below are 3 different varieties of octagons. A avoid sign is an instance of objects in daily life the is in the shape of one octagon.

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Octagon classifications

Like other polygons, one octagon can be divide as regular or irregular. If every the sides and interior angles of an octagon are equal, the is a regular octagon. Otherwise that is an rarely often rare octagon.

Regular octagonIrregular octagon
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All sides and also interior angles are equalNot all sides and also angles are equal

Octagons and other polygon can additionally be classified as either convex or concave. If all internal angles of one octagon or polygon are much less than 180°, it is convex. If one or much more interior angle are larger than 180°, that is concave. A continuous octagon is always a convex octagon.

Convex octagonConcave octagon
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All inner angles 180°

Parts of one octagon

Diagonals of an octagon

A diagonal line is a line segment joining two non-consecutive vertices. 5 diagonals deserve to be attracted from every vertex. A complete of 20 diagonals deserve to be attracted for one octagon. The following figure is an example.

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Internal angles of an octagon

The amount of the inner angles of one octagon amounts to 1080°.

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As displayed in the number above, 5 diagonals have the right to be attracted to divide the octagon right into six triangles. The blue lines over show simply one means to division the octagon into triangles; there are others. The sum of internal angles that the 6 triangles amounts to the sum of internal angles the the octagon. Due to the fact that the amount of the internal angles the a triangle is 180°, the amount of the interior angles for the hexagon is 6 × 180° = 1080°.

Regular octagons

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

Since each of the eight internal angles in a regular octagon space equal in measure, each inner angle measures 1080°/8=135° as displayed below.
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Each exterior angle for a constant octagon has an same measure. The exterior angle of a continuous octagon have actually an angle of 45°.
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Symmetry in continual octagons

A consistent octagon has 8 present of symmetry and a rotational the opposite of bespeak 8. This method that it have the right to be rotated in together a means that it will look the exact 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 the rotation

Area of a constant octagon

The area of a continual octagon with side length s is:

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. Accordingly, the side size of the square is
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. The area that the octagon deserve to be calculated by individually the locations of the 4 right triangles from the area of the square.