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Octagon (8gon)
From Greek: okto "eight" + gonia "angle"
Try this
Adjust the octagon below by dragging any orange dot. By clicking on the top left command line,
you can switch it between a
regular and
irregular octagon.
Because an octagon has an even number of sides, in a
regular octagon, opposite sides are
parallel.
Properties of regular octagons
Interior angle 
135° 
Like any regular polygon, to find the interior angle we use the formula
(180n–360)/n . For an octagon, n=8.
See Interior Angles of a Polygon 
Exterior Angle 
45° 
To find the exterior angle of a regular octagon, we use the fact that the exterior angle
forms a
linear pair
with the interior angle, so in general it is given by the formula
180interior angle.
See Exterior Angles of a Polygon 
Area 
4.828s^{2} approx

Where S is the length of a side.
To find the exact area of an octagon or any polygon, using various methods,
see Area of a Regular Polygon and
Area of an Irregular Polygon 
Properties of all octagons
Number of diagonals 
20 
The number of distinct diagonals possible from all vertices. (In general ½n(n–3) ).
In the figure above, click on "show diagonals" to see them.
See Diagonals of a Polygon 
Number of triangles 
6 
The number of triangles created by drawing the diagonals from a given vertex. (In general n–2).
In the figure above, click on "show triangles" to see them. See Triangles of a Polygon 
Sum of interior angles 
1080° 
In general 180(n–2) degrees .
See Interior Angles of a Polygon 
The Octagon Houses
Houses and rooms are sometimes built in an octagonal shape (pronounced: "ockTAGonall"), perhaps because they
feel somewhat like a circular space but are made of straight wall sections which are easier to build.
While no longer so popular, there are examples that are being preserved as historic buildings.
The one on the right is the
Loren Andrus Octagon House in Washington, Michigan USA, built in 1860.
Because they are based on a regular octagon, opposite walls are parallel and the rooms have a pleasing symmetry.
Related polygon topics
General
Types of polygon
Area of various polygon types
Perimeter of various polygon types
Angles associated with polygons
Named polygons
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