Mensuration Maths- Definition
A branch of mathematics that talks about the length, volume, or area of
different geometric shapes is called Mensuration. These shapes exist either in
2-dimensions or 3-dimensions. Let’s learn the difference between the two.
Differences Between 2D and 3D shapes
2D Shape 3D Shape
If a shape is surrounded by three If a shape is surrounded by a no. of
or more straight lines in a plane, surfaces or planes then it is a 3D shape.
then it is a 2D shape.
These shapes have no depth or These are also called solid shapes and
height. unlike 2D they have height or depth.
These shapes have only two These are called Three dimensional as
dimensions say length and they have depth (or height), breadth and
breadth. length.
We can measure their area and We can measure their volume, Curved
Perimeter. Surface Area (CSA), Lateral Surface Area
(LSA), or Total Surface Area (TSA).
Mensuration in Maths - Important Terminologies
Let’s learn a few more definitions related to this topic.
Terms Abbreviation Unit Definition
m2 or The area is the surface which is
Area A
cm2 covered by the closed shape.
cm or The measure of the continuous line
Perimeter P m along the boundary of the given
figure is called a Perimeter.
cm3 or The space occupied by a 3D shape is
Volume V
m3 called a Volume.
m2 or If there’s a curved surface, then the
Curved
CSA cm2 total area is called a Curved Surface
Surface Area
area. Example: Sphere
m2 or The total area of all the lateral
Lateral cm2 surfaces that surrounds the given
LSA
Surface area figure is called the Lateral Surface
area.
m2 or The sum of all the curved and
Total Surface
TSA cm2 lateral surface areas is called the
Area
Total Surface area.
m2 or The area covered by a square of
Square Unit –
cm2 side one unit is called a Square unit.
m3 or The volume occupied by a cube of
Cube Unit –
cm3 one side one unit
Mensuration Formulas
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. Students can also download the mensuration formulas
list PDF from the link given above. In general, the most common formulas in
mensuration involve surface area and volumes of 2D and 3D figures.
Mensuration Formulas For 2D Shapes
Area Perimeter
Shape Figure
(Square units) (units)
Square a2 4a
Rectangle l×b 2 ( l + b)
Circle πr2 2πr
Area Perimeter
Shape Figure
(Square units) (units)
√[s(s−a)(s−b)
Scalene (s−c)],
a+b+c
Triangle Where, s =
(a+b+c)/2
Isosceles
½×b×h 2a + b
Triangle
Equilateral
(√3/4) × a2 3a
triangle
Area Perimeter
Shape Figure
(Square units) (units)
b+
Right Angle
½×b×h hypotenuse +
Triangle
h
Rhombus ½ × d1 × d2 4 × side
Parallelogra
b×h 2(l+b)
m
Trapezium ½ h(a+c) a+b+c+d
Mensuration Formulas for 3D Shapes
Curved
Surface
Total
Area (CSA)
Volume Surface
or Lateral
Shape (Cubic Area (TSA) Figure
Surface
units) (Square
Area (LSA)
units)
(Square
units)
Cube a3 LSA = 4 a2 6 a2
LSA = 2h(l + 2 (lb +bh
Cuboid l×b×h
b) +hl)
Sphere (4/3) π r3 4 π r2 4 π r2
Curved
Surface
Total
Area (CSA)
Volume Surface
or Lateral
Shape (Cubic Area (TSA) Figure
Surface
units) (Square
Area (LSA)
units)
(Square
units)
Hemisphere (⅔) π r3 2 π r 2 3 π r 2
Cylinder π r 2 h 2π r h 2πrh + 2πr2
Cone (⅓) π r2 h πrl πr (r + l)
