September 29, 2023

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 formulas 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= Semi-circle 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 l= slant height base x height perimeter of base x slant height lateral surface area+base area Cone l=slant height,   h =height , r= radius of base area of base x height= Frustum of a cone lateral surface area+ 