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, AL 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)
AL = (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, AL 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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