"The Pentagon" refers to the building that houses offices of the United States Department of Defence. "the pentagon" refers to a specific five sided figure
The Pentagon is located near Washington DC in Arlington, Virginia (United States of America) and is called the pentagon because it is a five sided building.
They are both 2 dimensional objects with five straight sides and five angles. The sum of the internal angles is 540 degrees, the sum of the exterior angles is 360 degrees.