
Pentagon (5gon)
From Greek: pente "five" + gonia "angle"
Definition: A polygon with 5 sides
Try this
Adjust the pentagon below by dragging any orange dot. By clicking on the top left command line,
you can switch it between a
regular and
irregular pentagon.
Properties of regular pentagons
Interior angle 
108° 
Like any regular polygon, to find the interior angle we use the formula
(180n–360)/n . For a pentagon, n=5.
See Interior Angles of a Polygon 
Exterior Angle 
72° 
To find the exterior angle of a regular pentagon, 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 
1.72 S^{2} approx

Where S is the length of a side.
To find the exact area of a regular pentagon or any regular polygon, using various methods,
see Area of a Regular Polygon and
Area of an Irregular Polygon 
Properties of all pentagons
Number of diagonals 
5 
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 
3 
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 
540° 
In general 180(n–2) degrees .
See Interior Angles of a Polygon 
The Pentagon
On the right is the wellknown headquarters building for the US Department of Defense 
commonly known as "The Pentagon" due to its shape.
As you can see, it has several rings of offices inside.
These, in geometric terms, would be called concentric regular pentagons, since they share a common center point
and are symmetrical the way a regular polygon is.
It was built in 1943, has 17.5 miles (28 Km) of corridors,
and a floor area of 6,500,000 square feet (604,000 m^{2}).
In 1992, the Pentagon became a National Historic Landmark.
Other polygon topics
General
Types of polygon
Area of various polygon types
Perimeter of various polygon types
Angles associated with polygons
Named polygons
(C) 2009 Copyright Math Open Reference. All rights reserved

