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:
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.
Perimeter is the quantity, which deals with the outer boundary of the closed figure.
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 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).
You can download mensuration formulas pdf class 10th
All Mensuration Formulas
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.
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
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 90o angle) to each other like shown in figure below.
Two-dimensional figure with four sides and all four sides are equal and opposite sides are parallel.
Trapezium is the closed figure consist of four sides among which two opposite sides are parallel to each other.
· 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.
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.
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.
= (2.π.r.h) +(2.π.r2)
Cone is a folded tip, tent like 3D shape as shown in figure below. It has a circular base.