Important Formulas of Mensuration

(2-D Figures)

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

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

Trigonometry: Basic Concepts, Formulas

(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

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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