Pyramids (Formula and concept)

Pyramids

When we think of pyramids we think of the Great Pyramids of Egypt. They are actually Square Pyramids, because their base is a Square.

Parts of a Pyramid

A pyramid is made by connecting a base to an apex

Types of Pyramids

There are many types of Pyramids, and they are named after the shape of their base.

	Pyramid	Base
Triangular Pyramid:			Details >>
Square Pyramid:
Pentagonal Pyramid:

Right vs Oblique Pyramid

This tells you where the top (apex) of the pyramid is. If the apex is directly above the center of the base, then it is a Right Pyramid, otherwise it is an Oblique Pyramid.

Right Pyramid	Oblique Pyramid

Regular vs Irregular Pyramid

This tells us about the shape of the base. If the base is a regular polygon, then it is a Regular Pyramid, otherwise it is an Irregular Pyramid.

Regular Pyramid	Irregular Pyramid
Base is Regular	Base is Irregular

Area and Volume

The Volume of a Pyramid 1/3 × [Base Area] × Height The Surface Area of a Pyramid When all side faces are the same: [Base Area] + 1/2 × Perimeter × [Slant Length] When side faces are different: [Base Area] + [Lateral Area]

Notes On Surface Area The Surface Area has two parts: the area of the base (the Base Area), and the area of the side faces (the Lateral Area). For Base Area : It depends on the shape, there are different formulas for triangle, square, etc. For Lateral Area : When all the side faces are the same: Just multiply the perimeter by the "slant length" and divide by 2. This is because the side faces are always triangles and the triangle formula is "base times height divided by 2" But if the side faces are different (such as an "irregular" pyramid) then add up the area of each triangular shape to find the total lateral area.