A WebQuest for high school age students in Geometry

Designed by: Dan Royster

The Pentagon Building, headquarters of the Department of Defense of the United States Government, lies just across the Potomac River from Washington D.C. in Arlington, Virginia. It is one of the world’s largest office buildings. It has three times the floor space of the Empire State Building in New York City. Although it was completed on January 15, 1943, it is still thought of as one of the most efficient office buildings in the world.

The Department of Defense has asked your firm, Treacherous Neutralizing Technologies, to develop a Covert Automated Missile Launching System, or C.A.M.L.S. (pronounced "camels"), that would enable The Pentagon to defend itself, and be capable of providing viable covert reinforcements to other military operations around the world using surface-to-air missiles.

Your firm, TNT, plans to construct a Subterranean (underground) Missile storage, Loading, and Launching System or SMLLS (pronounced "smiles"). The missiles are stored in a basement underneath the actual Pentagon Building. An operator positioned at a remote location within the building can activate, load, and fire missiles from his location to any predetermined and preprogrammed location. Upon activating the system, missiles travel in succession along an underground track from their storage location. The track makes a 90° turn at the apothem of The Pentagon Building and head toward the center of The Pentagon, located within the courtyard where the missiles are loaded automatically onto the subterranean launch pad which then carries the missile to the surface and launches them at will.

Your task as a group, working for the engineering development division of Treacherous Neutralizing Technologies, is to perform the dimensional analysis of The Pentagon and sketch an artist’s rendering demonstrating what your firm plans to do.

You will perform some dimensional analysis to create an architectural-type rendering of what your firm, TNT, plans to do. However, this is a top-secret operation and you will need to use and possibly develop other acronyms and code words to discuss the project. Your team is covering Covert Missile Firing, or CMF, and will develop the specifications necessary for CAMLS. In the interest of secrecy, you will refer to your firm as the Turkish Nomadic Taxi (TNT) providing CAMELS (CAMLS) to Catch My Fade (CMF).

Upon completion of this project, you will have at least two diagrams on at least a 36 in. By 36 in. Posterboard or some form of a digital presentation media, demonstrating what the CAMLS looks like installed and in action at The Pentagon. Your diagrams will be clearly labeled with the specifications you have determined will work with the actual Pentagon Building. Please keep your Geometry textbook handy, along with a calculator, to assist you in this process.

• What is the measure of a central angle of The Pentagon? This will be used to calculate the apothem.
• Calculate the apothem of The Pentagon from its center in the courtyard to the outer edge of the building. This will indicate how far the missiles must travel to reach the launch pad and how far a missile must travel to ‘clear the building’ if its firing line is the apothem.
• Calculate the distance from the outer edge of a vertex on the building to the center in the courtyard. This will indicate how far the missiles must travel to ‘clear the building’ if its firing line is a vertex.
• Calculate the angle of elevation from the surface at the center of The Pentagon in the courtyard to the top of the inner wall of The Pentagon Building. This will indicate the minimum angle at which a missile can be fired without hitting the building.

3. The Drafting Technician and the Artist will construct two diagrams. One will illustrate the path a missile will travel underground as it travels along the apothem and is loaded onto the launch platform. The other diagram will illustrate a missile being fired from the launch pad in the courtyard at the center of The Pentagon Building and detailing the minimum and maximum angles of elevation from which the missiles can be launched.
4. Each group will present their findings, along with their illustrations, to the class.

By completing this Webquest, you are applying what you know regarding the properties of physical shapes. This is what geometry is all about. You also would have used some trigonometry. Did you notice that most of the calculations involved triangles? The properties of triangles are extremely useful in many real life applications. In fact, if you continue your studies into trigonometry, you will learn about the concept called triangulation. Of course, this webquest was designed to get you to use and apply the principles learned in geometry and see that is does have real life application. However, it also involved much more than that.

This webquest dealt with science and science fiction. It required you to explore the web and use technology. I hope you also now have an appreciation for The Pentagon Building, because it is an architectural wonder. Did you know before completing this webquest that The Pentagon is the control center of all military operations and that it is so massive in size that it is considered a city within itself? Did you find yourself reading more about The Pentagon Web site than what was required to complete this project?

Finally, this project taught you some life skills. It taught you to research and use resources, to apply the academic knowledge you already have, to compile your information, and present it to others. These are all useful life skills. So, to answer your question, "When will I ever use this stuff, Mr. Royster?" The answer is everyday.

McDougal Littell, Inc., (2001). Geometry - Chapter 1 & Chapter 11 Resource Book.

We all benefit by being generous with our work. Permission is hereby granted for other educators to copy this WebQuest, update or otherwise modify it, and post it elsewhere provided that the original author's name is retained along with a link back to the original URL of this WebQuest. On the line after the original author's name, you may add Modified by (your name) on (date). If you do modify it, please let me know and provide the new URL.