Pentagon (5-gon)
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
180-interior angle.
See
Exterior Angles of a 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
The Pentagon
Above is the well-known 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 m2).
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
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