MENSURATION: DEFINITION, FORMULAS AND PROPERTIES
What is Mensuration?
Mensuration is a branch of mathematics that studies various geometrical shapes, sizes, area, length, height, width, volume, surface area, and lateral surface area. It highlights the principles of calculations and formulas for different shapes and figures. Any closed figure with sides and vertices is included in mensuration.
Mensuration is all about defining and describing the characteristics of both 2D and 3D closed geometric shapes. They are categorized according to their size, shape, and density as 2D and 3D figures are different from each other in terms of their plane and degrees. It mostly deals with different types of quadrilaterals and properties.
What is a 1D Figure?
1DFigures are simple geometric shapes that only exist in one dimension. They only use one measurement. Examples of one-dimensional figures are:
A line (an arrow at the end enclosing it).
A segment of a line, enclosed at both ends by a point.
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Difference between 2D and 3D figures
| 2D Figures | 3D Figures |
|---|---|
|
2D figures have two planes namely the x-axis and the y-axis. |
3D figures have three planes namely the x-axis, y-axis, and z-axis. |
|
These figures do not include depth or height. |
These figures have an account of depth and height while calculating. |
|
2D figures exist in two-dimensional space. |
3D figures exist in three-dimensional space. |
|
These figures are bounded by two or more straight lines. |
These figures are surrounded by several straight lines and surfaces. |
|
Length, breadth and perimeter are the measurements used. |
Length, breadth, height, volume, curved surface area, lateral surface area, and total surface area are the measurements used. |
|
Edges are clearly visible in the 2D figures |
Edges may overlap or be hidden from view in 3D Figures. |
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Mensuration Formulas
2D Figures
Conclusion
We have covered all the geometric characteristics of 2D and 3D figures. There might be a lot of formulae to recall but it can be made simpler when we visualise how the formulas were developed in accordance with the requirements and shape.
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Frequently asked questions
1. What does length, breadth, and height mean?
- Length is defined as the measure of distance between two points. It is applicable for both 2D and 3D figures and measured in mm, cm, m, and km.
- Breadth is defined as the width of a 2D or a 3D figure.The breadth of a figure is usually smaller than the length and has similar units of measurement as length.
- Height is defined as the vertical distance from the base to the top of a 3D figure.
2. Difference between area and volume?
- Area is defined as a closed geometric figure occupied by area. It is applicable for both 2D and 3D figures and measured in the squared length units.
- Volume is mostly used for 3D figures. The volume gives us an idea of what a 3D figure holds.
3. What is surface area and its types?
- Surface area is defined as the area of the surface of a 3D figure.
- Lateral surface area – Lateral surface area covers all sides of the 3D objects except the top and base of the object
- Total surface area is defined as the sum of surface areas of the total 3D object including the top and base.
