## Important Formulas of Mensuration

Contents

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

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