Mensuration is a mathematical concept that calculates the surface area and volume of an object. The word ‘mensuration’ is a Greek word meaning ‘to measure.’ The concept of Mensuration uses algebraic equations to calculate the width, volume, and depth of an object. Even though mathematicians considered the calculations as an estimated value, studies have proven that the calculation done by Mensuration is comparatively more accurate than the physical measurement of an object.
Mensuration is then classified into two categories –
- Plane Mensuration – This aspect of Mensuration deals with the calculation of perimeter and area of plane objects like rectangle, polygon, hexagon, etc. They are also known as 2D shapes.
- Solid Mensuration – In this aspect of Mensuration, the surface area and volume of a solid figure is calculated. For example – cylinder, cuboid, cone, etc. They are also known as 3D shapes.
To calculate Mensuration it is essential to understand the difference between 2D objects and 3D objects –
| 2D Objects | 3D Objects |
| 2D objects only have length and breadth | 3D objects have length, breadth, and depth |
| 2D objects can be measured in the Perimeter and Area. | 3D objects can be measured in Volume, Curved Surface Area, Lateral Surface Area, and Total surface Area |
| 2D objects have visible edges because they don’t overlap with each other. | 3D objects do not have complete visible edges because they overlap each other. |
| 2D objects are used for parallel projection and a one-point perspective. | 3D objects are used in orthographic projection and tow/three-point perspective. |
Every term of Mensuration calculation has a different unit of measurement. These units of measurements are critical, and one must always keep them in consideration. To trick students in examinations, teachers formulate questions of objects in different units of measurement. To get an accurate answer, the conversion of units is necessary. Here is a list of terms and their unit of measurement –
| Term | Unit of Measurement |
| Area | m2 or cm2 |
| Perimeter | m or cm |
| Volume | m3 or cm3 |
| Square Unit | m2 or cm2 |
| Cube Unit | m3 or cm3 |
| Total Surface Area | m2 or cm2 |
| Lateral Surface Area | m2 or cm2 |
| Curved Surface Area | m2 or cm2 |
The concept of Mensuration has designed different formulas for different objects. By inserting the values in the formulas, one can quickly get an answer to any Mensuration problem.
Mensuration formula’s for 2D and 3D objects –
2D OBJECTS
| Object Shape | Area | Perimeter |
| Square | a2 | 4a |
| Rectangle | l × b | 2 (l+b) |
| Circle | πr2 | 2 π r |
| Equilateral Triangle | (√3/4) × a2 | 3a |
| Isosceles Triangle | ½ × b × h | 2a + b |
| Scalene Triangle | √[s(s−a)(s−b)(s−c)] | a+b+c |
| Right-angle Triangle | ½ × b × h | base + hypotenuse +height |
| Rhombus | ½ × d1 × d2 | 4 × side |
| Parallelogram | b × h | 2(l+b) |
| Trapezium | ½ h(a+b) | a+b+c+d |
3D OBJECTS
| Object Shape | Volume | CSA/LSA | TSA |
| Cube | a3 | – | 6 a2 |
| Cuboid | lˣwˣh | – | 2 (lb +bh +hl) |
| Cylinder | π r 2 h | 2π r h | 2πrh + 2πr2 |
| Cone | (⅓) π r2 h | π r l | πr (r + l) |
| Sphere | (4/3) π r3 | 4 π r2 | 4 π r2 |
| Hemisphere | (⅔) π r3 | 2 π r2 | 3 π r2 |
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