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Mensuration is a key idea in mathematics that investigates the measuring of various geometric shapes and figures. Mensuration formulas are useful in a variety of competitive tests. It aids us in comprehending the dimensions of various two-dimensional and three-dimensional things. A 2D shape has only two dimensions, length, and breadth, whereas a 3D figure has three dimensions: length, breadth, and height. The two most common characteristics we measure for 2D shapes are area (A) and perimeter (P).Volume(V), total, lateral, and curved surface area are all estimated in 3D.
Definition
Mensuration is a field of mathematics that investigates the measuring of 2D and 3D figures based on factors such as length, volume, shape, surface area, and so on. In other words, it is the measurement method that is based on algebraic equations and mathematical formulas.
Let us learn more about mensuration, and the formulas, and solve a few cases to better understand it.
Mensuration Formulas for 2D Figures
2D shapes are plane figures that are fully flat and have only two dimensions – length and width – in geometry. They have no thickness and can only be measured in two dimensions.
|
Shape name |
Area |
Perimeter (or Circumference) |
|
Circle |
πr² |
2πr |
|
Square |
a² |
4a |
|
Rectangle |
l × b |
2(l + b) |
|
Triangle |
½ × height × base |
a + b + c |
|
Parallelogram |
b × h |
2(l + b) |
|
Rhombus |
½ × d1 × d2 |
4 × side |
|
Trapezium |
½ × h (a + b) |
a + b + c + d |
Mensuration Formulas for 3D Figures
A three-dimensional shape or solid with faces, edges, and vertices is referred to as a 3D shape. They have a surface area that includes all of their faces. The volume of these shapes is determined by the space they occupy.3D shapes include the cube, cuboid, cone, and cylinder, and real-world examples include a book, a party hat, and a coke tin.
|
Shape Name |
TSA |
LSA (or CSA) |
Volume |
|---|---|---|---|
|
Cube |
6a² |
4a² |
a³ |
|
Cuboid |
2 (lb +bh +hl) |
2h (l + b) |
l × b × h |
|
Cone |
πr (r + l) |
πrl |
(⅓) × πr²h |
|
Cylinder |
2πrh + 2πr² |
2πrh |
πr² h |
|
Sphere |
4πr² |
4πr² |
(4/3) × πr³ |
|
Hemisphere |
3πr² |
2πr² |
(⅔) × πr³ |
Uses of Mensuration
Mensuration is an important topic with a wide range of applications in real-world situations.
Volumes necessary for packaging milk, liquids, and solid edible food items are measured.
Surface area measurements are essential for estimating the cost of painting houses, buildings, and other structures.
Optimum cost packaging sachets for milk and other products, such as tetra packaging.
Accurate measurement of agricultural fields and floor spaces is necessary for purchase/sale operations.
Water levels and amounts in rivers and lakes can be determined using volumes and heights.
Important Mensuration Terms
Mensuration is concerned with the measurement of planar and solid shapes. Let us look at some of the key terms:
-
Area: A two-dimensional figure’s area is the amount of space it takes up. It is measured in square units.
-
Perimeter: Perimeter is the overall distance around the shape or the length of any closed shape’s boundary. It is measured in square units.
-
Volume: A 3D shape’s volume is the amount of space it takes up. It is measured in cubic meters.
-
Surface Area: Surface Area is the entire area filled by a 3D object’s surfaces. Curved or Lateral Surface Area and Total Surface Area are the two types.
Important points
-
The use of solid shapes and nets can aid in the measurement of an object. Faces, edges, and vertices will be easier to understand if you use solid shapes. Nets will aid in the visualization of 3D shape structures.
-
When an object is measured with a non-standard unit of measurement, mensuration and measurement must be mastered jointly.
-
Mensuration is a branch of mathematics that studies the calculation of geometric figures and their parameters, such as area, length, volume, lateral surface area, and surface area, among others.
-
It covers all of the essential equations and properties of a wide range of geometric shapes and figures, as well as the mathematical foundations.
