|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|
|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|
|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|
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.