**Important Formulas of Mensuration**

__(2-D Figures)__

__(2-D Figures)__

**Rectangle**

Area = length × breadth

Perimeter = 2(L + B)

Diagonal = (l^{2} + b^{2})^{1/2}

**Square**

Area = (side)^{2} = ½ (diagonal)^{2}

Perimeter = 4 × side

Diagonal = sqrt(2) × side

**Rhombus**

Area = b × h = ½ d_{1} × d_{2}

**Parallelogram**

Area = base × height

**Trapezium**

Area = ½ (sum of parallel sides) × (altitude)

**Quadrilateral**

Area of Quadrilateral = ½ × diagonal × (sum of altitudes on diagonals)

*For Triangles- click here*

**Circle**

Radius = ½ (diameter)

Circumference = 2 × π × r = π × d [π = 22/7 or 3.14]

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

Area = π × r^{2}

Area of Sector = π × r^{2} × θ/360 (θ = sector angle)

Area of Sector = ½ × length of arc × radius

Area of Segment = Area of Sector – Area of Triangle

**(3-D Figures)**

**Cuboid**

Lateral Surface Area = 2 × (l + b) × h

Total Surface Area = 2 × (lb + lh + hl)

Diagonal = (l^{2} + b^{2} + h^{2})^{1/2}

Volume = l × b × h

**Cube**

Lateral Surface Area = 4 × a^{2}

Total Surface Area = 6 × a^{2}

Diagonal = a √3

Volume = (side)^{3}

**Cylinder**

Lateral Surface Area = 2 π × r h

Total Surface Area = 2 π × r (r + h)

Volume = π × r^{2} h

**Cone**

Lateral Surface Area = π × r × l

Here l = (r^{2} + h^{2})^{1/2} ; [l = slant height]

Total Surface Area = π × r (r + l)

Volume = 1/3 π × r^{2} h

**Sphere**

Lateral Surface Area = 4 π × r^{2}

Total Surface Area = 4 π × r^{2}

Volume = 4/3 π × r^{3}

Volume of Spherical Shell = 4 π × (R^{3} – r^{3})

**Hemisphere**

Lateral Surface Area = 2 π × r^{2}

Total Surface Area = 3 π × r^{2}

Volume = 2/3 π × r^{3}

__Important Unit Conversions__

__Important Unit Conversions__

1 are = 100 m^{2}

1 hectare = 10000 m^{2}

I hectare = 100 ares

100 hectare = 1 km^{2}

1 cm^{3} = 1 ml

1 m^{3} = 1000 litre

1000 cm^{3} =1 litre

**Frustum**

l = [h^{2} + (R^{ –} r)^{2} ]^{1/2}

Volume = 1/3 π × h (R^{2} + r^{2 }+Rr)

Curved Surface Area = π × l × (R + r)

Total Surface Area = π × l × (R + r) + πR^{2} + πr^{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 = (2/3)^{1/2} × side

Volume = √2/12 (side)^{3}

Curved Surface Area = 3 × √3/4 × (side)^{2}

Total Surface Area = √3 (side)^{2}

**Pyramid**

Volume = 1/3 × Area of base × height

Curved Surface Area = ½ × Perimeter of Base × slant height

Total Surface Area = CSA + Area of Base