Expert: Josh - 3/2/2004

Question
Mari made a model of a prism whose base has 9 sides. How many edges and how many faces did her model have?

Also

Matt made a model of a pyrmid with 16 edges. How many sides did the base of his pyrmid have?

Answer
Well, you know what a prism looks like. It has a bottom and a top cover. Each of the side of the base, rises straight up to give the prism some elevation (or height).

The bottom line is that it has 2 + S faces, where S equals the number of sides the base has and the 2 accounts for the top and bottom plate.

The number of edges is given by 3S (i.e., three times S). Draw a picture to convince yourself -- starting with a triangular prism, then, the rectangular prism and so forth.
You can even construct a model with some toothpicks and glue (3M blue-tak will do). Use the sticks to build the skeleton, each one should represent an edge in the prism structure.

Again, why not develop some intuition by building a simple model yourself? A prism (by definition) contains a base and a point, P, centered in the middle and elevated to a certain height. Each corner of the base connects with this point P. So, the number of edges is given by 2S.
S edges coming from the sides of the base, another S edges act like wires joining the vertices to point P.

Ans: octagonal pyramid.