**Important Mensuration Formula**

Mensuration is and important branch of mathematics. In this we basically calculate the perimeter, area, volume, etc of the geometrical figures such as Square, Triangle, Cube, Cubiod, Sphere, cone, etc.

In this article we will list the important and frequently used mensuration formula of 2-dimensional and 3-dimensional fiogures both.

**Mensuration Formula of 2-D Figures**

Let us first look at the important mensuration formula of 2-D figures such as square, triangle, rectangle, paralleogram, kite, etc.

**Rectangle**

**Area**= length × breadth**Perimeter**= 2(L + B)**Diagonal**= \sqrt { { l }^{ 2 }+{ b }^{ 2 } }

**Square**

**Area**= (side)² = \frac { 1 }{ 2 } { \times d }^{ 2 }**Perimeter**= 4 × side**Diagonal**= \sqrt { 2 } \times { side }

**Rhombus**

- Area = b × h = \frac { 1 }{ 2 } { side\times }{ side }

**Parallelogram**

**Area**= base × height**Perimeter =**sum of lengths of all sides

**Trapezium**

Area = \frac { 1 }{ 2 } \times \left( sum\quad of\quad parallel\quad sides \right) \times \left( Altitude \right)

**Quadrilateral**

Area of Quadrilateral = \frac { 1 }{ 2 } \times \left( diagonal \right) \times \left( sum\quad of\quad Altitudes\quad on\quad diagonal \right)

**Circle**

Radius = \frac { diameter }{ 2 }

Circumference = 2\times \pi \times r = \pi \times d [π = 22/7 or 3.14]

**Note- Perimeter of circle is called Circumference (C)**

Area = { \pi }{ r }^{ 2 }

Area of Sector = { \pi }r^{ 2 }\times \frac { \theta }{ 360 } (θ = sector angle)

Area of Sector = \frac { 1 }{ 2 } \times \left( length\quad of\quad arc \right) \times \left( radius \right)

Area of Segment = Area of Sector – Area of Triangle

**Also Read: ****Trigonometry: Basic Concepts, Formulas**

**Mensuration Formula of 3-D Figures**

**Cuboid**

Lateral Surface Area = 2\times \left( length+breadth \right) \times \quad height

Total Surface Area = 2\times \left( lb+bh+hl \right)

Diagonal = \sqrt { { l }^{ 2 }+{ b }^{ 2 }+{ h }^{ 2 } }

Volume = \left( l\times b\times h \right)

**Cube**

Lateral Surface Area = 4\times { a }^{ 2 }

Total Surface Area = 6\times { a }^{ 2 }

Diagonal = \sqrt { 3 } a

Volume = { (side) }^{ 3 }

**Cylinder**

Lateral Surface Area = 2\pi rh

Total Surface Area = 2\pi { r }\left( r+h \right)

Volume = \pi { r }^{ 2 }h

**Cone**

Lateral Surface Area = \pi rl

Here l = \sqrt { { r }^{ 2 }+{ h }^{ 2 } } ; [l = slant height]

Total Surface Area = \pi r\left( r+h \right)

Volume = \frac { 1 }{ 3 } \pi { r }^{ 2 }h

**Sphere**

Lateral Surface Area = 4\pi { r }^{ 2 }

Total Surface Area = 4\pi { r }^{ 2 }

Volume = \frac { 4 }{ 3 } \pi { r }^{ 3 }

Volume of Spherical Shell = 4\pi \left( R^{ 3 }-{ r }^{ 3 } \right)

**Hemisphere**

Lateral Surface Area = 2\pi { r }^{ 2 }

Total Surface Area = 3\pi { r }^{ 2 }

Volume = \frac { 2 }{ 3 } \pi { r }^{ 3 }

**Frustum**

l=\sqrt { { h }^{ 2 }+{ (R-r) }^{ 2 } }

Volume = \frac { 1 }{ 3 } \times \pi \times h\left( { R }^{ 2 }+{ r }^{ 2 }+Rr \right)

Curved Surface Area = \pi \times l\left( R+r \right)

Total Surface Area = \pi \times l\left( R+r \right) +\pi { R }^{ 2 }+\pi { r }^{ 2 }

**Prism**

Volume = Area of base × height

Curved Surface Area (CSA) = Perimeter of Base × height

Total Surface Area = CSA + 2 × Area of Base

**Tetrahedron**

- It is made up of 4 equilateral triangles.

height = \frac { \sqrt { 2 } }{ 3 } \times side

Volume = \frac { \sqrt { 2 } }{ 12 } ({ side) }^{ 3 }

Curved Surface Area = 3\times \frac { \sqrt { 3 } }{ 4 } \times ({ side })^{ 2 }

Total Surface Area = \sqrt { 3 } \times ({ side })^{ 2 }

**Pyramid**

Volume = \frac { 1 }{ 3} × Area of base × height

Curved Surface Area = \frac { 1 }{ 2 } × Perimeter of Base × slant height

Total Surface Area = CSA + Area of Base

**Important Unit Conversions**

Let us not forget these important conversions. You should remember these converions, and these are often used in many examples.

- 1 are = 100 m²
- 1 hectare = 10000 m²
- I hectare = 100 ares
- 100 hectare = 1 km²
- 1 cm³ = 1 ml
- 1 m³ = 1000 litre
- 1000 cm³ = 1 litre

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