Important Mensuration Formula
Mensuration is and important branch of mathematics. In this we basically calculate the perimeter, area, volume, etc of the geometrical figures such as Square, Triangle, Cube, Cubiod, Sphere, cone, etc.
In this article we will list the important and frequently used mensuration formula of 2-dimensional and 3-dimensional fiogures both.
Mensuration Formula of 2-D Figures
Let us first look at the important mensuration formula of 2-D figures such as square, triangle, rectangle, paralleogram, kite, etc.
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
- Perimeter = sum of lengths of all sides
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
Also Read: Trigonometry: Basic Concepts, Formulas
Mensuration Formula of 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
Let us not forget these important conversions. You should remember these converions, and these are often used in many examples.
- 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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