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In Geometry, an object having width, height and depth is referred to as a 3D solid object. A 3D solid object that is only bound by flat faces is known as a polyhedron.

Definition of Pyramid

A pyramid is defined as a polyhedron that has a polygon as its base and three or more triangular faces that meet at a point. This point is called the apex of the pyramid.

Types of pyramids

Pyramids can be either right pyramids or oblique pyramids.

If the apex is exactly over the center of the base of the pyramid then it is known as a right pyramid.

If the apex is not exactly over the center of the base of the pyramid, then it is known as an oblique pyramid. In an oblique pyramid the faces are not congruent.

                                                                                                                                        

Volume of a Pyramid
The volume of a pyramid is defined as the number of cubic units that will exactly fill the pyramid.

If b is the base area of the pyramid and h is the height of the pyramid, then the volume of the pyramid is given by the formula
Volume = ⅓  bh

The base area of the pyramid is calculated depending on the type of polygon that forms the base.

The volume is expressed in cubic units.

Practice questions:

Question: Find the volume of a pyramid which has a height equal to 5 cms and a square base with sides equal to 6 cms.
( Answer:    Area of the base of the pyramid b = 6 * 6 (area of a square)
        Height of the pyramid h = 5 cms
        Volume of the pyramid     = ⅓ * 36 * 5
                    = 60 cubic cms
)

Question: Find the volume of a pyramid with height equal to 6 cms and a square base with sides equal to 4 cms.
( Answer:  32 cubic cms ) 

Area of the Pyramid

The surface area of a right pyramid is calculated as the sum of the surface area of the base of the pyramid and the surface areas of each of the faces of the pyramid.

In case of a right square pyramid, if b is the length of side of the base of the pyramid, and s is the slant of the pyramid, then the area of the pyramid is given by the formula = b2 + 2bs.

The area of the pyramid is measured in sq cms.

Practice questions:

Question: Find the surface area of a square pyramid with base sides equal to 10 cms and slant equal to 11 cms.
( Answer:    Base side of the pyramid b = 10 cms
Slant of the pyramid s = 11 cms
Area of the pyramid     = 10 * 10 + 2 * 10 * 11
=  100 + 220
=  320 sq cms    
)

Question: Find the surface area of a square pyramid with base sides equal to 14 cms and its slant is equal to 10 cms.
( Answer:     Base side  of the pyramid b = 14 cms
        Slant of the pyramid = 10 cms
        Area of the pyramid     = 14 * 14 + 2 * 14 * 10
                    = 196 + 280
                    = 476 sq cms
)

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