06prisms

= Prisms =

A ** prism ** is a 3 Dimensional shape where
 * the two ends are congruent (same shape, same size)
 * the cross-section is congruent throughout its length.

A ** prism ** is named by the shape of its end (or cross-section)

Total Surface Area of Prisms (TSA)
The TSA of any prism equals the sum of the area of all the faces.

A prism consists of two ends plus some rectangles. The number of rectangles is given by the number of sides in the end shape.
 * A triangular prism has 2 ends + 3 rectangles = 5 faces
 * A quadrilateral prism has 2 ends + 4 rectangles = 6 faces
 * A pentagonal prism has 2 ends + 5 rectangles = 7 faces

For most prisms there is no simple rule to use for calculating the Total Surface Area.
 * TSA = find the area of every face and add them up
 * Look for shortcuts where two or more faces are the same (the ends are always the same)

Euler's Formula for Polyhedrons
Euler's Formula for Polyhedrons works for prisms. Prisms are one type of polyhedron.


 * Euler's Formula says that
 * ** V – E + F = 2 **
 * Where
 * **V** = Vertices (corners)
 * **[[image:bhs-methods10/06rubickscube.gif width="287" height="304" align="right"]]E** = Edges
 * **F** = Faces

Example

 * A cube has
 * 8 vertices
 * 12 edges
 * 6 faces


 * so Euler's Formula becomes
 * 8 – 12 + 6 = 2

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