Memorable Geometry

On our 8th grade East Coast trip, we visited the Washington Monument.  I was able to take a lot of great photos of it and was also able to find some hidden geometry.  The part of the monument outlined in red is a right rectangular prism.  It's a bit hard to see, but imagine looking down on it from the sky.  This prism makes up the base of the monument and it has four lateral faces.  It also has four lateral edges and two bases.  Theorem 12-1 states that the lateral area of a right prism equals the perimeter of a base times the height of the prism, or L.A. = ph.  Theorem 12-2 states that the volume of a right prism equals the area of a base times the height of the prism or V = Bh.  Finally, the surface area of the prism equals the lateral area plus 2 times the area of the base.

On the very top of the monument rests a pyramid.  It is outlined in blue in the picture.  It also has four lateral faces and lateral edges.  The pyramid's vertex acts as the top of the monument and it shares one of the prism's 2 bases.  Theorem 12-3 states that the lateral area of a regular pyramid equals half of the perimeter of the base times the slant height or L.A. = 1/2pl.  Theorem 12-4 states that the volume of a pyramid equals one third the area of the base times the height of the pyramid or V = 1/3Bh.  Lastly, the surface area of the pyramid equals the lateral area plus the area of the base.  So, not only does the Washington Monument represent one of our greatest founding fathers, but it represents the beauty of geometry. ~MG1