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The most Important Formulas used in Mensuration

The most Important Formulas used in Mensuration:Mensuration is one of the most important topics in Quantitative Aptitude. Now a day’s questions coming from this topic in all competitive exams. Here we are providing you some most important formulas which is used in mensuration which are useful in SSC, IBPS, UPSC, Railways and other competitive exams.

The most Important Formulas used in Mensuration
The most Important Formulas used in Mensuration
 AREAPERIMETER
Rectanglel×b2(l+b)
Square a×a4a
Parallelograml × h2(l+b)
Triangleb×h/2 or √s(s-a)(s-b)(s-c) here s=a+b+c/2a+b+c
Right angle Triangle 1/2(bh)b+h+d
Isosceles right angle triangle ½. a22a+d  where d=a√2
Equilateral Triangle √3. a2/4 or  ½(ah)….where h = √3/23a
Trapezium1/2h(a+b)Sum of all sides
Rhombusd1 × d2/24l
Quadrilateral1/2 × Diagonal × (Sum of offsets)
Kited1×d2/22 × Sum on non-adjacent sides

 

Frustum :

  • Curved surface area = πh(r1+r2)
  • Surface area = π( r12+ h(r1+r2) + r22)

Circle :

  • Area =  πr^2 or πd^2/4
  • Circumference = 2πr  or πd
  • Area of sector of a circle = (θπr^2 )/360

Cube :

  • Volume: V = l3
  • Lateral surface area = 4a2
  • Surface Area: S = 6s2
  • Diagonal (d) = √3l

Cuboid :

  • Volume of cuboid: lbh
  • Total surface area = 2 (lb + bh + hl) or 6l2
  • Length of diagonal =√(l^2+b^2+h^2)

Right Circular Cylinder :

  • Volume of Cylinder = π r2h
  • Lateral Surface Area (LSA or CSA) = 2π r h
  • Total Surface Area = TSA = 2 π r (r + h)
  • Volume of hollow cylinder = π r h(R2– r2)

Right Circular cone :

  • Volume = 1/3 π r2h
  • Curved surface area: CSA=  π r l
  • Total surface area = TSA = πr(r + l )

Sphere

  • Volume: V = 4/3 πr3
  • Surface Area: S = 4πr2

Hemisphere :

  • Volume = 2/3 π r3
  • Curved surface area(CSA) = 2 π r2
  • Total surface area = TSA = 3 π r2

Prism :

  • Volume = Base area x h
  • Lateral Surface area = perimeter of the base x h

Pyramid:

  • Volume of a right pyramid = (1/3) × area of the base × height.
  • Area of the lateral faces of a right pyramid = (1/2) × perimeter of the base x slant height.
  • Area of whole surface of a right pyramid = area of the lateral faces + area of the base.

Tetrahedron :

  • Area of its slant sides = 3a2√3/4
  • Area of its whole surface = √3a2
  • Volume of the tetrahedron = (√2/12) a 3

Regular Hexagon :

  • Area =  3√3 a2/ 2
  • Perimeter  = 6a

Some other Formula :

  • Area of four walls = 2h(l+b)
  • Area of Pathway running across the middle of  a rectangle = w(l+b-w)
  • Perimeter of Pathway around a rectangle field = 2(l+b+4w)
  • Area of Pathway around a rectangle field =2w(l+b+2w)
  • Perimeter of Pathway inside a rectangle field =2(l+b-4w)
  • Area of Pathway inside a rectangle field =2w(l+b-2w)

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