Why does The Pentagon have five sides?

Answer 1

A five sided figure is called a pentagon. The root of the word penta- comes from the Greek word for five. The Pentagon (the building which is the HQ for the US Department of Defense), was originally planned to be built on some land that was roughly pentagonal in shape, according to the Wikipedia article. Another parcel of land was eventually chosen as the site, but they liked the idea of the design, so they kept it.

Answer 2

By the summer of 1941, the War Department work force in the Washington, D.C. area numbered more than 24,000 civilian and military personnel housed in 17 buildings and was expected to reach 30,000 by the beginning of 1942. Providing office space for the workers was part of the military construction mission of the Quartermaster Corps' Construction Division, already struggling to cope with the vast mobilization construction underway before the United States entered World War II.

The federal government considered constructing temporary buildings, but Brigadier General Brehon B. Somervell, an aggressive Engineer officer who headed the construction division, had another idea. On Thursday, 17 July 1941, he summoned two of his subordinates, Lieutenant Colonel Hugh J. Casey, also an Engineer officer, and George E. Bergstrom, a prominent civilian architect, and told them that by Monday morning he wanted basic plans and an architectural perspective for an air-conditioned office building to house 40,000 workers in four million square feet of space, not more than four stories high, with no elevators. Indeed, Lieutenant Colonel Casey and his staff completed the basic layout of a five-sided building by that following Monday, after what he later described was "a very busy weekend."

-The five sided design maximizes efficiency of the space available. Despite 17.5 miles of corridors it takes only seven minutes to walk between any two points in the building.