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.
Contents
Mensuration formulas for 2D shapes:
Name  Figure  Area  Perimeter 
Rectangle  l= length, b=breadth  
Square  a= side , d= diagonal 
If d is given , then 
4 x side= 4a 
Triangle
(scalene) 
b =base, h= height or altitude of a triangle 
(i)
(ii) Heron’s Formula 
a+b+c 
Equilateral triangle  a= side , h= height or altitude  (i)
(ii) 
3a 
Quadrilateral  AC=diagonals
altitudes on AC from the vertices D and B respectively. 
(i)
(ii) product of diagonals x sin of the angle between them 
AB+BC+CD+AD 
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 
2(a+b) 
Rhombus  a=each equal sides , and are the diagonals  4a  
Trapezium  a, b are parallel sides
h is the perpendicular distance between parallel sides 
AB+BC+CD+DA  
Circle  r=radius ,  circumference=  
Semicircle  r =radius  
Sector of a circle  o centre , r= radius
l=length of arc AB, = angle of the sector 
(i)
(ii) 
l+2r 
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 
Cube  a=side/edge  
cuboid  l=length, b=breadth, h=height  lbh  
Right circular cylinder  r= radius of base
h=height 

Right triangular prism  area of base x height  perimeter of base x height  lateral surface area+2(area of base)  
Sphere  r=radius  
Hemisphere  r= radius  
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+ 
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