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
