# Prisms and Pyramids

Prisms and pyramids are important members of polyhedron family.

**Prism**

A prism is a special type of polyhedron. It has two ends which is of same shape and size. These ends are parallel to each other and are separated by rectangles. A prism is named according to the base of the prism.

The bases of the prism ABCDE and abcde are equal polygons which are parallel to each other. The faces are the rectangles AabB, BbcC, CcDd, DdEe and EeAa.

Aa, Bb, Cc etc. are called lateral edges.

Prisms are classified according to their bases.

**Triangular prism: **Triangular prism is composed of two triangular base and three rectangular sides.

**Pentagonal prism : **If the base of the prism is pentagon, then the prism is called pentagonal prism.

A prism is called a right prism if the lateral edges are perpendicular to bases if they are not, it is called oblique prism.

**Pyramid**

A solid shape with triangular side faces meeting at a common vertex and having polygonal base. Some pyramids have square bases. Eg: Egyptian pyramid. They are called as square pyramid. A triangular pyramid is also known as a tetrahedron.

Pyramids are classified based on the base of the prymaid.

**Triangular Pyramid (tetrahedron): **If the base of the pyramid is triangular in shape they are called tetrahedron.

**Square pyramid:** If the base of the pyramid is a square then they are called square pyramid.

**Hexagonal pyramid:** A pyramid has a hexagon as its base.

Tabulate the number of faces, edges and vertices for the following polyhedron:

Solid |
F |
V |
E |
F + V |
E + 2 |

Cube
Cuboid Tetrahedron Octahedran Egyptian pyramid |
6
6 4 8 5 |
8
8 4 6 5 |
12
12 6 12 8 |
14
14 8 14 10 |
14
14 8 14 10 |

Here V stands for number of vertices, F stands for number of faces and E stands for number of edges.

From the last two columns we find that F + V = E + 2.

∴ F + V - E = 2

This relation is called Euler's formula. This formula is true for any polyhedron.