Generic selectors
Exact matches only
Search in title
Search in content
Post Type Selectors

Mensuration formulas in Maths

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

Mensuration formulas in Maths

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.

Learn some amazing Maths Tricks

Three-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.

AREA:

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.

Searching a for a Good Mathematics Tutor?

PERIMETER:

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:

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.

Want to learn Mathematics Concept?

SURFACE AREA:

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.

Difference between Perimeter, Surface Area and Volume:

IMPORTANT MENSURATION FORMULAS FOR CLASS 8TH, 9TH, 10TH PDF

Important Mensuration Formulas for class 8th and 9th

Table: Important mensuration formulas for class 8th and 9th

Class 8t h to 10th 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.

Important Mensuration formulas for class 8th, 9th, 10th pdf RECTANGLE:

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 10th

RECTANGLE:

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:

SQUARE:

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

Important properties are:

  • All sides are equal.
  • Consecutive sides are perpendicular
  • Perimeter= 4a
  • Area=a2

RHOMBUS

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

Important properties are:

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

TRAPEZIUM

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

Important properties are:

  • 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)

CUBE

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.

Important properties of cube are:

  • Cube has all sides equal
  • It has 6 faces and 12 edges.
  • Volume= a3
  • CSA= 4a2
  • TSA= 6a2

CUBOID

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.

Important properties of Cuboid are

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

CYLINDER

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.

Important properties Cylinder are

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

= (2.π.r.h) +(2.π.r2)

  • Volume= π r2.h

CONE

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

Important properties of CONE are:

  • Volume= 1/3. π r2.h
  • TSA= π.r.l + π r2
  • CSA= π.r.l
SHARE:

    May be you like it

    5-Step Guide to find the Best Home Tuition in Gwalior

    5-Step Guide to find the Best Home Tuition in Gwalior

    By Truemaths Tech, on 22 Jun, 2023

    Become a Mathematics Genius in 15 Days

    Become a Mathematics Genius in 15 Days

    By Truemaths Tech, on 13 Jun, 2023

    Improve your mathematics with Vedic Maths Classes

    Improve your mathematics with Vedic Maths Classes

    By Truemaths Tech, on 17 Jun, 2023

    Maths Tuition in ISBT Dehradun

    Maths Tuition in ISBT Dehradun

    By Truemaths Tech, on 27 Jun, 2023

    Parents Reviews

    Student Reviews

    In the beginning, when I came across The Doon School Entrance Exam coaching, I was not very sure about it. Later, when I read the testimonials and contacted these people in person. Then, I got the required trust. I started the classes with a firm belief and see, now I have cleared the exam. Thank you so much.

    doon school result

    Aayansh Pandey

    Doon School

    The day I was sitting in the examination hall and took the paper in my hand, I was surprised. Most of the questions, I have already studied while my preparation. Thanks to the Experts who with their sheer hard work have made my journey so smooth.

    Doon school result

    Hridit Rohit Surana

    Doon School

    It was my immense luck and fortune to get the coaching from Truemaths for the preparation of Welham Girls'. All the teachers leave no stone unturned to shape my future.

    Welham girls result

    Tamanna

    Welham Girls' School

    Huge respect, love, and devotion to entire teachers, mentors, and experts for their blessings and hard work towards me. It's their efforts that make me to count myself into better professionals.

    the doon school result by truemaths

    Madhav Ramesh

    The Doon School

    Truemaths has been a great contributor to the development of my personality. I have established my leadership, time management, and team skills and to get the Final selection in The Doon School.

    Sahil Truemaths

    Sahil Patil

    St. George's School


    Newsletter

    STAY INFORMED & INSPIRED

    Subscribe to our Newsletter

    Got some doubts or queries?

    Schedule a one-on-one session with our Experts.

    Join WhatsApp Community