March 2, 2024

Mensuration Formulas for 2D and 3D Shapes PDF Download

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.

Mensuration Formulas Chart

Mensuration formulas for 2D -shapes:

Name Figure Area   Perimeter
Rectangle      l= length,   b=breadth
l \times b
a= side ,   d= diagonal

If d is given , then A=\frac{d^{2}}{2}

4 x side= 4a



b =base,    h=  height or altitude of a triangle

(i) \frac{1}{2}\times b\times h

(ii)  Heron’s Formula


Equilateral triangle  a= side , h= height or  altitude    h=\frac{\sqrt{3}}{2} \times a
(i) \frac{1}{2}\times a\times h

(ii) \frac{\sqrt{3}}{4}a^{2}

Quadrilateral AC=diagonals

h_{1}, h_{2}

altitudes on AC from the vertices D and B respectively.


(i)  \frac{1}{2}\times AC\times (h_{1}+h_{2})


(ii) \frac{1}{2}\times product of diagonals x sin of the angle between them

a and b be the lengths of parallel sides and h be the height
(i)Area= base x  height

(ii) area= absin\theta  , \theta

is the angle between the sides of the parallelogram
Rhombus       a=each equal sides  ,                                        d_{1}
  and d_{2}
  are the diagonals
\frac{1}{2}\times d_{1}\times d_{2}
Trapezium a, b are parallel sides

h is the perpendicular distance between parallel sides

\left ( \frac{a+b}{2} \right ) \times h
Circle    r=radius , \pi=\frac{22}{7}
\pi r^{2} circumference=2\pi r
Semi-circle            r =radius \frac{1}{2}\pi r^{2}
\pi r+ 2r
Sector of a circle
o  centre   , r= radius

l=length of arc AB,  \theta= angle of the sector

l=2\pi r.\frac{\theta }{360^{\circ}}

(i) \pi r^{2}\frac{\theta }{360^{\circ}}

(ii) \frac{1}{2}r\times l

Regular hexagon   a= each of the equal side \frac{3\sqrt{3}}{2}a^{2}
Regular octagon a= each of the equal side 2a^{2}\left ( 1+\sqrt{2} \right )


Mensuration formulas for 3D -shapes:

Name Figure Volume Lateral /Curved surface area Total surface Area
Cube    a=side/edge a^{3}
4a^{2} 6a^{2}
cuboid  l=length, b=breadth,  h=height lbh 2(l+b)h
Right circular cylinder
r= radius of base 


\pi r^{2} 2\pi rh
2\pi r(h+r)
Right triangular prism
area of base x height perimeter of base x height lateral surface area+2(area of base)
Sphere   r=radius \frac{4}{3}\pi r^{3}
4\pi r^{2}
  r= radius
\frac{2}{3}\pi r^{3} 2\pi r^{2}
3\pi r^{2}

l= slant height

\frac{1}{3}\timesbase x height \frac{1}{2}\times
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=\frac{1}{3}\pi r^{2}h
\pi rl
\pi rl+\pi r^{2}
Frustum of a cone 
\frac{1}{3}\pi h(r^{2}+Rr+R^{2}) \pi l(r+R)
lateral surface area+ \pi (R^{2}+r^{2})

Download PDF:

Mensuration Formulas pdf


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