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8.5 Pyramids

A pyramid is a polygon with all the vertices joined to a point outside the plane of the polygon.

If the polygon is regular then the pyramid is called a regular pyramid and is named by the polygon which forms its base.

If the base is a square the pyramid is called a regular square pyramid, if it is a pentagon the pyramid is called a regular pentagonal pyramid and so on and so forth.

The parts of the pyramid are named analogous to the geometric solids mentioned earlier in the chapter. It is a base, lateral faces, lateral edges and an altitude.

The terminology varies only for the vertex. In all the geometric solids seen so far all corners are called vertices. In a pyramid however the apex to which all corners of the polygon are joined is called the vertex of the pyramid.

A regular pyramid has a property called slant height which is the perpendicular distance between the vertex and any side of the polygon.

The lateral area of a regular pyramid is defined using this parameter.

Lateral area of a regular pyramid = square units

where ’p’ is the perimeter and ’ l’ is the slant height.

Figure 8.8

In pyramid PABC, P is the vertex and PR is the slant height.

     Perimeter      =   l (seg. AB) + l (seg. BC) + l (seg. CA)

     = p


8.1 Introduction to solid geometry
8.2 Prism
8.3 The cuboid and the cube
8.4 Cylinders
8.5 Pyramids
8.6 Right circular cone
8.7 Sphere

Chapter 9

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