Pentagon

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Regular pentagon 1

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Richmond pentagon 1

Regular Pentagon Using Carlyle Circle

01-Pentagon-Euklid Animation

Overhand-folded-ribbon-pentagon

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Symmetries of pentagon

Pentagon refers to a geometric shape and is also widely recognized as the name of the headquarters of the United States Department of Defense. This article will focus on both aspects, providing a comprehensive overview of the geometric figure and the iconic building.

Pentagon (Geometry)

A pentagon is a five-sided polygon with five straight sides and five angles. In geometry, pentagons can be regular or irregular. A regular pentagon has all sides of equal length and all interior angles equal to 108 degrees. The study of pentagons is a part of geometry, a branch of mathematics that deals with the properties and relations of points, lines, surfaces, and solids.

Properties

A regular pentagon has several unique properties, including:

• The sum of the interior angles of a pentagon is 540 degrees.
• A pentagon can be divided into three triangles, which is useful in calculating its area.
• The area (A) of a regular pentagon with side length (a) can be calculated using the formula: \(A = \frac{1}{4} \sqrt{5(5+2\sqrt{5})} a^2\).

Pentagon (Building)

The Pentagon is the headquarters of the United States Department of Defense, located in Arlington County, Virginia, near Washington, D.C.. It is one of the world's largest office buildings, with about 6.5 million square feet of office space, accommodating approximately 23,000 military and civilian employees and about 3,000 non-defense support personnel.

History

Construction of the Pentagon began on September 11, 1941, and was completed on January 15, 1943. The building was designed by American architect George Bergstrom and built by contractor John McShain. It was constructed to consolidate the offices of the U.S. Department of War, now known as the Department of Defense.

Architecture

The Pentagon is shaped like a regular pentagon and is composed of five concentric rings, A through E, with ring E being the outermost. The building's design facilitates the efficient movement of personnel between offices. It has five floors above ground and two basement levels. Each of the building's five sides has its own entrance, and the central courtyard is approximately 5 acres in size.

Significance

The Pentagon is not only a symbol of the American military but also a representation of the country's strength and resilience. It has been the site of several historic events, including a significant portion of the building being damaged during the September 11 attacks in 2001. The Pentagon has since been repaired and continues to serve as a key location for U.S. defense planning and operations.