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**Formula used in Mensuration**

Mensuration is one of the topics in Quants. Now a days questions coming from this chapter also. Here we are providing you Some important formulas which is used in mensuration which are useful in SSC, Railways and other exams.

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**Rectangle :**

- Area = lb
- Perimeter = 2(l+b)

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**Square :**

- Area = a×a
- Perimeter = 4a

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**Parallelogram**

- Area = l × h
- Perimeter = 2(l+b)

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**Triangle :**

- Area =b×h/2 or √s(s-a)(s-b)(s-c)…………….where s=a+b+c/2

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**Right angle Triangle :**

- Area =1/2(bh)
- Perimeter = b+h+d

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**Isosceles right angle triangle :**

- Area = ½. a
^{2} - Perimeter = 2a+d……………………….where d=a√2

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**Equilateral Triangle :**

- Area = √3. a
^{2}/4 or ½(ah)….where h = √3/2 - Perimeter = 3a

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**Trapezium :**

- Area = 1/2h(a+b)
- Perimeter = Sum of all sides

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**Rhombus :**

- Area = d1 × d2/2
- Perimeter = 4l

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**Quadrilateral**

- Area =1/2 × Diagonal × (Sum of offsets)

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**Kite :**

- Area = d1×d2/2
- Perimeter = 2 × Sum on non-adjacent sides

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**Circle :**

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

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**Frustum :**

- Curved surface area = πh(r
_{1}+r_{2}) - Surface area = π( r
_{1}^{2}+ h(r_{1}+r_{2}) + r_{2}^{2})

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**Cube :**

- Volume: V = l
^{3} - Lateral surface area = 4a
^{2} - Surface Area: S = 6s
^{2} - Diagonal (d) = √3l

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**Cuboid :**

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

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**Right Circular Cylinder :**

- Volume of Cylinder = π r
^{2}h - 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(R
^{2}– r^{2})

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**Right Circular cone :**

- Volume = 1/3 π r
^{2}h - Curved surface area: CSA= π r l
- Total surface area = TSA = πr(r + l )

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**Sphere**

- Volume: V = 4/3 πr
^{3} - Surface Area: S = 4πr
^{2}

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**Hemisphere :**

- Volume = 2/3 π r
^{3} - Curved surface area(CSA) = 2 π r
^{2} - Total surface area = TSA = 3 π r
^{2}

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**Prism :**

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

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**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.

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**Tetrahedron :**

- Area of its slant sides = 3a
^{2}√3/4 - Area of its whole surface = √3a
^{2} - Volume of the tetrahedron = (√2/12) a
^{3}

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**Regular Hexagon :**

- Area = 3√3 a
^{2}/ 2 - Perimeter = 6a

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**Some other Formula :**

- 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)
- Area of four walls = 2h(l+b)

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