Important Formulas of Mensuration

(2-D Figures)

Rectangle

Area = length × breadth

Perimeter = 2(L + B)

Diagonal = (l2 + b2)1/2

Square

Area = (side)2 = ½ (diagonal)2

Perimeter = 4 × side

Diagonal = sqrt(2) × side

Rhombus

Area = b × h = ½ d1 × d2

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 × r2

Area of Sector = π × r2 × 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 = (l2 + b2 + h2)1/2

Volume = l × b × h

Cube

Lateral Surface Area = 4 × a2

Total Surface Area = 6 × a2

Diagonal = a √3

Volume = (side)3

Cylinder

Lateral Surface Area = 2 π × r h

Total Surface Area = 2 π × r (r + h)

Volume = π × r2 h

Cone

Lateral Surface Area = π × r × l

Here l = (r2 + h2)1/2   ; [l = slant height]

Total Surface Area = π × r (r + l)

Volume = 1/3 π × r2 h

Sphere

Lateral Surface Area = 4 π × r2

Total Surface Area = 4 π × r2

Volume = 4/3 π × r3

Volume of Spherical Shell = 4 π × (R3 – r3)

Hemisphere

Lateral Surface Area = 2 π × r2

Total Surface Area = 3 π × r2

Volume = 2/3 π × r3

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

Frustum

l = [h2 + (R r)2 ]1/2

Volume = 1/3 π × h (R2 + r2 +Rr)

Curved Surface Area = π × l × (R + r)

Total Surface Area = π × l × (R + r) + πR2 + πr2

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