Mensuration is a branch of mathematics that deals with the study of different geometrical shapes, their perimeter,area , surface area, curved surface area, volume etc. Basically, there are two type of geometric shapes (i) 2D shapes (ii) 3D shapes
2D shapes are : circle, square, rectangle, square , parallelogram, rhombus etc.
3D shapes are : cube , cylinder, cone , cuboid, sphere , prism , pyramid , cone etc.
Now let’s learn all the important mensuration formulas involving 2D and 3D shapes. Using this mensuration formula list, it will be easy to solve the mensuration problems.
Mensuration formulas for 2D -shapes:
|Square||a= side , d= diagonal||
If d is given , then
|4 x side= 4a|
b =base, h= height or altitude of a triangle
(ii) Heron’s Formula
|Equilateral triangle||a= side , h= height or altitude||(i)
altitudes on AC from the vertices D and B respectively.
(ii) product of diagonals x sin of the angle between them
|Parallelogram||a and b be the lengths of parallel sides and h be the height||(i)Area= base x height
(ii) area= , is the angle between the sides of the parallelogram
|Rhombus||a=each equal sides , and are the diagonals||4a|
|Trapezium|| a, b are parallel sides
h is the perpendicular distance between parallel sides
|Sector of a circle||o centre , r= radius
l=length of arc AB, = angle of the sector
|Regular hexagon||a= each of the equal side||6a|
|Regular octagon||a= each of the equal side||8a
Mensuration formulas for 3D -shapes:
|Name||Figure||Volume||Lateral /Curved surface area||Total surface Area|
|cuboid||l=length, b=breadth, h=height||lbh|
|Right circular cylinder||r= radius of base
|Right triangular prism||area of base x height||perimeter of base x height||lateral surface area+2(area of base)|
|Pyramid||base x height||perimeter of base x slant height||lateral surface area+base area|
|Cone||l=slant height,||area of base x height=|
|Frustum of a cone||lateral surface area+|
Download PDF: mensuration formulas-pdf
You might also be interested in: