# Mensuration

Mensuration is the branch of mathematics which studies the measurement of the geometric figures and their parameters like length, volume, shape, surface area, lateral surface area, etc.

## Mensuration Maths - Definition

A branch of mathematics which talks about the length, volume or area of different geometric shapes is called Mensuration. These shapes exist in 2 dimension or 3 dimensions. Let’s learn the difference between the two.

Difference Between 2D and 3D shapes

2D Shape 3D Shape
If a shape is surrounded by three or more straight lines in a plane, then it is a 2D shape. If a shape is surrounded by a no. of surfaces or planes then it is a 3D shape.
These shapes have no depth or height. These are also called as solid shapes and unlike 2D they have both height or depth.
These shapes have only 2-D length and breadth. These are called Three dimensional as they have depth, breadth and length.
We can measure their area and Perimeter. We can measure their volume, CSA, LSA or TSA.

## Mensuration in Maths- Important Terminologies

 Area A M2 / cm2 The area is the surface which is covered by the closed shape. Perimeter P Cm / m The measure of the continuous line along the boundary of the given figure is called a Perimeter. Volume V Cm3/ m3 In a 3D shape, the space included is called a Volume. Curved Surface Area CSA M2 / cm2 If there’s a curved surface, then the total area is called a Curved Surface area. Example: Sphere or Cylinder. Lateral Surface area LSA M2 / cm2 The total area of all the lateral surfaces that surrounds the figure is called the Lateral Surface area. Total Surface Area TSA M2 / cm2 If there are many surfaces like in 3D figures, then the sum of the area of all these surfaces in a closed shape is called Total Surface area. Square Unit – M2 / cm2 The area covered by a square of side one unit is called a Square unit. Cube Unit – M3 / cm3 The volume occupied by a cube of 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:

Shape Area (Square units) Perimeter (units) Figure
Square a2 4a
Rectangle l × b 2 ( l + b)
Circle πr2 2 π r
Scalene Triangle

√[s(s−a)(s−b)(s−c)],

Where, s = (a+b+c)/2

a+b+c
Isosceles Triangle ½ × b × h 2a + b
Equilateral Triangle (√3/4) × a2 3a
Right Angle Triangle ½ × b × h b + hypotenuse + h
Rhombus ½ × d1 × d2 4 × side
Parallelogram b × h 2(l+b)
Trapezium ½ h(a+b) a+b+c+d

### Mensuration Formulas for 3D Shapes

Shape Volume (Cubic units) Curved Surface Area (CSA) or Lateral Surface Area (LSA) (Square units) Total Surface Area (TSA) (Square units) Figure
Cube a3 6 a2
Cuboid l × w × h 2 (lb +bh +hl)
Sphere (4/3) π r3 4 π r2 4 π r2
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 π r l πr (r + l)

### Mensuration Problems

Question: Find the area and perimeter of a square whose side is 5 cm?

Solution:

Given:

Side = 5 cm

Area of a square = a2 square units

Substitute the value of “a” in the formula, we get

Area of a square = 52
A = 5 . 5 = 25

Therefore, the area of a square = 25 cm2

The perimeter of a square = 4a units

P = 4 . 5 =20

Therefore, the perimeter of a square = 20 cm.

### What is mensuration in Maths?

In maths, mensuration is defined as the study of the measurement of various 2D and 3D geometric shapes involving their surface areas, volumes, etc.

### What is the difference between mensuration and geometry?

Mensuration refers to the calculation of various parameters of shapes like the perimeter, area, volume, etc. whereas, geometry deals with the study of properties and relations of points and lines of various shapes.

### What are 2D and 3D Mensuration?

2D mensuration deals with the calculation of various parameters like area and perimeter of 2-dimensional shapes like square, rectangle, circle, triangles, etc.

3D mensuration is concerned with the study and calculation of surface area, lateral surface area, and volume of 3-dimensional figures like cube, sphere, cuboid, cone, cylinder, etc.