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

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.

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:

mensuration formulas class 10 pdf

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

IMPORTANT TERMINOLOGY RELATED TO MENSURATION: LENGTH AND BREADTH:

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.

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.

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:

difference between areaperimetervolume

You can download mensuration formulas pdf class 10th

All Mensuration Formulas

mensuration questions and answers for class 10

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

area of square
Area of 3d shapes in maths
area and perimeter of 3d shapes
mesuration formula for class 9th10th 1
mesurations formulas 1

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.

rectengle formula

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.

square formula

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.

Rhombus formula

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.

trapezium formula

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.

Cube formula

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.

Cuboid formula

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.

cylinder formula

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.

Cone formula

Important properties of CONE are:

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

For the Registration fill form



    SHARE:


    Leave a Reply

    Your email address will not be published.

      Get a Callback

      And our experts will help you to get through your queries and Crack the Exam




      Truemaths is a digital platform for almost all your learning needs. From Boarding schools' entrance exams to home tuitions. We have everything to cater to you with the best of facilities and services.
      We understand that every child has different learning needs. So, we have a group of Home tutors who work with students of different behavior, opinion, understanding, and learning abilities. This ensures special attention and care to every individual kid. Our tutors come to your door to make the learning flexible and convenient.
      We also prepare your kid for challenging entrance exams at different boarding schools. Not, only the written exam but we work out with students for the interview as well. Truemaths brush up on your child's intellect along with improving his communication skills.
      Not only this but we are there for the student from registration to preparation. We have experts who will fill the application forms of different schools for you and at the same time, prepare the student for the biggest battle.
      In addition to this, we have a specialized team of Mathematicians who have made learning Mathematics the easiest of all times. Our mission is to strengthen the weak fundamentals of students to get them rid of the fear of Maths.
      This is a dream of so many parents to send their child to the Defence Forces. Military schools serve this need. But, to get admission to these schools is a crooked cake. Truemaths get you sorted. We can prepare your kid for RIMC/RMS and Sainik school entrance examinations. As far as the coaching classes and study material is concerned, we keep everything ready for students.
      We, as mentors understand the psychology of students. So, our methodology is designed in such a way that it is scientifically proven and focuses on the understanding of concepts. We offer 3-Tier online assessments and tests, free video courses, and guaranteed improvement.

      Every child has a vivid approach to solve a certain query and as an educator, the best is to evaluate their approach of dealing with the problem instead of dominating them to solve the query our way.
      Truemaths believe in learning through games and activities. We try to engage students in such activities and fabricate the curriculum easily and interestingly. This helps students to have better visualization and grasp of verbal and non-verbal reasoning.

      We aim to help students to have a distinct and well-defined character and personality. This helps students to crack entrance exams of various boarding schools and Sainik schools. And at the same time, excel in their academic curriculum. We try to become a helping hand to students to have a definitive persona and to make them commendable young men and women of aura.