Finding the Volume of the Pentagon
The Pentagon in Arlington, Virginia, was named for the pentagonal shape of its horizontal cross
section. Each side of the Pentagon is 921 feet long, and the points where each pair of sides meet
are 783 feet from the center of the building. The Pentagon is 77 ft 3.5 in tall.
a) To find the volume occupied by the Pentagon, begin by finding the area of its base.
b) Use your answer to (a) to find the volume enclosed by the outer walls of the Pentagon.
c) Your answer to (b) is the volume enclosed by the outer walls of the Pentagon, but the
Pentagon is not a solid building. It has an open court space in the center, which is also in
the shape of a regular pentagon. At ground level, the court is 382 ft on a side with a
“radius” to each vertex of 325 ft. Find the volume of this inner court space and combine it
with your answer to (b) to find the actual volume of the Pentagon building.
Aerial overview of the Pentagon, with the Washington Monument in the distance. DoD photo by Master Sgt. Ken
Hammond, U.S. Air Force.
This picture may help you to think about how to find the area of a pentagon.
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Lesson from Developing Mathematics through Applications, Elementary, Preliminary Edition by N, Crisler and G. Simundza,
COMAP. Emeryville, CA. Key College Publishing, 2003.
Pentagon photo from Great Buildings website, http://www.greatbuildings.com/cgibin/gbi.cgi/The_Pentagon.html/cid_pentagon_usgov_01.html .
Pentagon picture from Area and Perimeter of Regular Polygons by M. Parsons and M. Greene,
http://jwilson.coe.uga.edu/EMAT6680/Parsons/MVP6690/Unit/Pentagon/pentagon.html