# Concepts and formulae of Pyramid and Tetrahedron for SSC CGL

## Detailed Concepts and formulae of Pyramid and tetrahedron for SSC CGL Exam

**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**, and

**2n 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.*

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Concepts and formulae of Pyramid and Tetrahedron for SSC CGL
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