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
(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