By Truemaths Tech, Last Updated 15 Jul, 2023 4 min read

**What is Mensuration in Maths?**

Mensuration is the branch of geometry, which deals with measurements of the forms associated with lines, areas, and volumes of one, two, and three-dimensional figures and structures.

**One-dimensional (1D) **mensuration deals with measurements, related to length and common figure is a line.

**Two-dimensional (2D) **deals with closed structures having a length and breadth extent in some other direction such as square, rectangle, parallelograms, triangles etc. The area and perimeter of the 2D shapes can be measured using mensuration formulas for different shapes.

T**hree-dimensional (3D) **closed structures along with length, breadth and height is there.

The Volumes and surface areas of the 3D shapes can be calculated with the help of different mensuration formulas for 3D structures.

Common calculations done in different figures mentioned below:

Important mensuration formulas from NCERT. The basics of mensuration needs to be understand by the Perimetrer, Area and Volume.

The length and breadth are the values we get when we measure the sides with a simple scale (Ruler). Measured in centimetre (cm), millimetre (mm), kilometre (km) etc.

The area is the quantity measured for closed figures only. In addition, it is a 2D property of the closed figure denoting what it can take inside it.

- Area is the extent of a piece of paper, land or any 2D closed surface.
- In simple language, we can say that area is quantity used to paint the wall, crop in the field and area that allows the air to come into through window, space on a page used to write. It depends on all lengths and breadths of the shape. Like in a window, if we change anyone of length or breadth keeping other same we get less or more air in the room.

Perimeter is the quantity, which deals with the outer boundary of the closed figure.

- For example, if we want to make a boundary of the field through a wire we will measure all the sides of the field or ground and add all the sides measured. The total wire used to make a boundary from all the sides is called a perimeter.

Volume is the quantity used for 3D structures like a ball, vessel and most of the things we see in our home. These structures have three quantities length, breadth and height.

- In simple language, any object which can contain any amount of substance in it. This capacity to contain that substance is known as volume.
- For example: Any solid body has a volume, which can be imagined as if the structure is made hollow or empty with outer body and filled with some liquid say water. This water carrying capacity is volume.

In 3D shapes, we see in our daily life, surface area is the outermost covering area of any shape. For example, if we see a matchbox (a cuboid like shape) the paper used to make that matchbox (that we see) is the surface area of the matchbox. Surface area has two components: Total Surface Area (TSA) and Curved Surface Area (CSA).

**Total Surface Area (TSA)**: It is the sum of all the area of the shape. Like what we have seen in example of matchbox.**Curved Surface Area (CSA)**is the sum of all the area around the shape but not roof and base.- Another easy way to understand the
**difference between Total Surface Area and Curved Surface Area**, if you want to paint your room, if you paint Curved Surface Area you will paint your all four walls but not roof and floor. However, if you calculate, Total Surface Area and paint your room you will be painting all four walls**including roof and floor.**

**Important Mensuration Formulas for class 8 ^{th} and 9^{th}**

Table: Important mensuration formulas for class 8^{th} and 9^{th}

Class 8^{t} ^{h} to 10^{th} NCERT of Maths has two-dimensional figures in syllabus like Square, rectangle, triangle, Rhombus, Trapezium and three-dimensional figures like a cube, cuboid, cylinder, cone, etc.

It is a four-sided figure with two opposite sides equal and consecutive sides are perpendicular. For example: shape of most of the windows and door. Click here for **Trigonometry formulas for class 10**th

It is a four-sided figure with two opposite sides equal and consecutive sides are perpendicular. For example: shape of most of the windows and door.

**Important properties are:**

Two-dimensional figure with four sides and all four sides are equal AND Two neighbouring sides are perpendicular (make 90^{o} angle) to each other like shown in figure below.

- All sides are equal.
- Consecutive sides are perpendicular
- Perimeter= 4a
- Area=a
^{2}

Two-dimensional figure with four sides and all four sides are equal and opposite sides are parallel.

- All sides are equal.
- Opposite sides are parallel
- Unlike square in a rhombus, consecutive sides are not perpendicular.
- Diagonals are cutting each other at 90
^{o}angle. - Perimeter= 4s
- Area= (side × height) = s×h

Trapezium is the closed figure consist of four sides among which two opposite sides are parallel to each other.

- Opposite sides are parallel
- Perpendicular distance between two parallel lines is called height (h).
- Perimeter= sum of all the sided= ab+bc+cd+da

· Area= ^{1}/2 ℎ𝑒𝑖𝑔ℎ𝑡. (𝑠𝑢𝑚 𝑜𝑓 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑠𝑖𝑑𝑒𝑠) = ^{1}/2 ℎ. (𝑎𝑏 + 𝑐𝑑)

A six faced shape with all the 12 edges equal is called as Cube. One common example Rubik’s Cube. All the sides are equal in Rubik’s cube.

- Cube has all sides equal
- It has 6 faces and 12 edges.
- Volume= a
^{3} - CSA= 4a
^{2} - TSA= 6a
^{2}

Cuboid is made up six rectangles i.e. it has a difference in its length, height and breadth. We can say in cuboid the measurement of all four parallel edges. It also has 6 faces, 8 vertices and 12 edges.

- CSA = 2(l×h+b×h)
- TSA= 2[(l×b)+(b×h)+(h×l)]
- Volume= l×b×h

It is one of the most commonly seen 3D shapes. Two exactly same circles are solidly connected to each other. For example, Pipes, body of most of the pens, etc. as shown in figure below.

- Curved Surface Area= 2.π.r.h
- Total Surface Area = CSA+ area of lower and upper base circles

= (2.π.r.h) +(2.π.r^{2})

- Volume= π r
^{2}.h

Cone is a folded tip, tent like 3D shape as shown in figure below. It has a circular base.

- Volume= 1/3. π r
^{2}.h - TSA= π.r.l + π r
^{2} - CSA= π.r.l

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