Concepts and formulae of Pyramid and Tetrahedron for SSC CGL

A Pyramid is a three-dimensional polyhedron of which one face is a polygon of any number of sides, and the other faces are triangles with a common vertex.

A pyramid with an n-sided base will have n + 1 vertices ,n + 1 faces , and2n edges.

**Right Pyramid: A right pyramid has its apex directly above the centroid of its base.

Regular Pyramid: A regular pyramid has a regular polygon base.

Generic Formulas:

Volume Of Pyramid = 1/3**× Base Area × Height**

Surface Area Of pyramid =1/2 × Perimeter of base × Slant Length

(only when all side faces are the same)

Surface Area = Base Area + Lateral Area
(When side faces are different)

Regular Right Pyramid with Square base ( pentahedron**):**

** A Square pyramid is a pyramid having a Square base and the other faces are all triangles.

There are (4+1) faces, 5 vertices and 8 edges in a pentahedron.

Formulas:

****

**** V = 1/3 Bh

where, e is the edge length, s is the slant height, h is the height, A is the Surface area, A L is the lateral Surface area, B is the area of the square base and a is the length of a side of the base.

Regular Right Pyramid with Triangular base (Tetrahedron):

** A triangular pyramid is a pyramid having a triangular base.

The tetrahedron is a triangular pyramid having congruent equilateral triangles for each of its faces.

There are 4 faces , 4 vertices and 6 edges in a tetrahedron.

**h =(√2)/(√3) ***** (Side)
**A L =(3√3)/4 * (Side)2

****A =(4√3) /4 * (Side)2

**V = (√2)****/ 12 * (Side)3 ** (Since V= 1/3 Bh )

_where, e is the edge length, s is the slant height, h is the height,__A L is the lateral Surface area,__A is the Surface area, V is Volume, B is the area of the base and a is the length of a side of the base.

|| Prism, || Cone, || Cylinder, || Sphere,Hemispheres, ||
|| Parallelepiped, || Pyramid ||