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Math Formulas | Square Prism Or Square Cuboid

Formula Math Square Prism Or Square Cuboid :
Area of Base [ A ] = s²
Perimeter of Base [ P ] = 4s
Surface Area of Prism = 2s² + 4sh = 2A + Ph
Volume of Prism = s²h = Ah
Note :
        s = side, h = height.


Example :
Question : Find the surface area and volume of a square prism with the given side 2 and height 4.

Answer : Find the area of the base.
Solution :  Area of the base [ A ] = s² = 2² = 4.

Answer : Find the perimeter of the base.
Solution : Perimeter of the base [ P ] = 4s = 4 x 2 = 8.

Answer : Find the surface area of prism.
Solution : Surface Area of Prism = 2A + Ph =  [2 x 4] + [8 x 4] = 8 + 32 = 40.

Answer : Find the volume of prism.
Solution : Volume of Prism = Ah = 4 x 4 = 16.

That is example will clearly how to calculate Formula Math the Volume, Surface Area, Perimeter of a Square Prism  Or Square Cuboid.

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Math Formulas | Cuboid Or Rectangular Prism

A Rectangular Prism/Cuboid is a solid figure bounded by six rectangular faces, a rectangular box. All angles are right angles, and opposite faces of a cuboid are equal. It is also a right rectangular prism.

Formula Math Rectangular Prism or Cuboid :
Area of Base [ A ] = l . w
Perimeter of Base (P) = 2l + 2w
Surface Area of Prism = 2[l.w] + [2l + 2.w] h
 = 2A + Ph
Volume of Prism = l.w.h = Ah
Diagonal of Prism = Sqrt [l² + w² + h²]

Note :
w = width, h = height , l = length

Example


Question : Find the surface area, volume and diagonal of a rectangular prism or Cuboid with the given length 2, width 3, height 4.

Answer : Find the area of the base.

Solution : Area of the base[A] = l . w = 2 . 3 = 6

Answer : Find the perimeter of the base.
Solution : Perimeter of the base [P] = 2l + 2w = [2 . 2] + [2 . 3] = 4 + 6 = 10

Answer : Find the surface area of prism.
Solution : Surface Area of Prism = 2.A + P.h = [2 . 6] + [10 . 4] = 12 + 40 = 52

Answer : Find the volume of prism.
Solution : Volume of Prism = A.h = 6 . 4 = 24

Answer: Find the diagonal of prism.
Solution : Diagonal of Prism = Sqrt [l² + w² + h²] = Sqrt [2² + 3² + 4²] = Sqrt [4 + 9 + 16] = Sqrt [29] = 5.39

That is example will clearly how to calculate the Formula Math Volume, Surface Area, Diagonal Perimeter of a Rectangular Prism or Cuboid.

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Math Formulas | Pentagonal Pyramid

FormulaMath
Formula Math Of Pentagonal Pyramid
Area of Base [ A ]= [ 5/2 ]a.s
Surface Area of Pyramid = [ 5/2 ]a.s + [ 5/2]s.l = A + [ 5/2 ]s.l
Volume of Pyramid = [ 5/6 ]a.b.h

Note :
s = side, h = height , l = length, 
a = apothem ,b = lant height


Example


Question : Find the surface area and volume of a pentagonal pyramid with the given apothem length 2, side 3, height 4 and the slant height 5.

Answer : Find the area of the base.
Solution : Area of the base [A] = [ 5/2 ]a.s = 5/2 . 2 . 3 = 15.

Answer :  Find the surface area of pyramid.
Solution : Surface Area of Pyramid = A + [ 5/2 ]s.l = 15 + [5/2] .3 . 5) = 15 + [5/2 x 15] = 15 + 37.5 = 52.5.

Answer : Find the volume of pyramid.
Solution :Volume of Pyramid = [ 5/6 ].a.b.h = [5/6] . 2 . 3 x 4 = (0.833) . 24 = 20.

That is  example will clearly how to calculate the Volume by Formula Math Surface Area of a Pentagonal Pyramid.

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Math Formulas | Triangular Prism

Formula MathFormula Math Of Triangular Prism Definition :

A Triangular Prism is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.
Formula Math Of Triangular Prism :

Area of Base [ A ]        =  ½ . a . b
Perimeter of Base [ P ] =  s.1 + s.2 + s.3
Surface Area of Prism  = a.b + [s.1+ s.2 + s.3].h = a.b + P.h
Volume of Prism           =  ½ . a . b . h = A.h
Note :
        a = altitude, b = base, h = height and s1, s2, s3 are sides

Example

Question : Find the surface area and volume of a triangular prism with the given altitude 2, base 3, height 4 and the sides 1, 2, 3.

Question : Find the area of the base.
Answer :   Area of the base [ A ] = ½ . a . b = 0.5 . 2 . 3 = 3.

 Question : Find the perimeter of the base.
 Answer :  Perimeter of the base [ P ] = s.1 + s.2 + s.3 = 1 + 2 + 3 = 6.
 Question : Find the surface area of prism.
 Answer :   Surface Area of Prism = a.b + P.h = [ 2 . 3 ] + [ 6 . 4 ] = 6 + 24 = 30.

Question : Find the volume of prism.
Answer :  Volume of Prism = A.h = 3 . 4 = 12.

That is  example Formula Math Of Triangular Prism Definition will clearly illustrates how to calculate the Volume, Surface Area, Perimeter of a Triangular Prism.

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