Before we move ahead to the list of important mensuration formulas, we need to discuss some important terms that constitutes these mensuration formulas.
Area (A) – The surface occupied by a given closed shape is called its area. It is represented by the alphabet A and is measured in unit square- m2/ cm2.
Perimeter (P) – The length of the boundary of a figure is called its perimeter. In other words, it is the continuous line along the periphery of the closed figure. It is represented by the alphabet P and is measures in cm/ m.
Volume (V) – The space that is contained in a three-dimensional shape is called its volume. In other words, it is actually the space that is enclosed in a 3D figure. It is represented by the alphabet V and is measured in cm3/ m3.
Curved Surface Area (CSA) – In solid shapes where there is a curved surface, like a sphere or cylinder, the total area of these curved surfaces is the Curved Surface Area. . The acronym for this is CSA and it is measured in m2 or cm2.
Lateral Surface Area (LSA) – The total area of all the lateral surfaces of a given figure is called its Lateral Surface Area. Lateral Surfaces are those surfaces that surround the object. The acronym for this is LSA and it is measured in m2 or cm2.
Total Surface Area (TSA) – The sum of the total area of all the surfaces in a closed shape is called its Total Surface Area. For example, in a cuboid when we add the area of all the six surfaces we get its Total Surface Area. The acronym for this is TSA and it is measured in m2 or cm2.
Square Unit (m2/ cm2) – One square unit is actually the area occupied by a square of side one unit. When we measure the area of any surface we refer to this square of side one unit and how many such units can fit in the given figure. It is expressed as m2 or cm2, depending on the unit in which the area is being measure.
Cube Unit (m3/ cm3) – One cubic unit is the volume occupied by a cube of side one unit. When we measure the volume of any figure we actually refer to this cube of side one unit and how many such unit cubes can fit in the given closed shape. It is written in m3 or cm3, depending on the unit that is being used to measure.
Now that our introduction to mensuration and the important terms is over let’s move to the mensuration formulas since this is a formula based topic. Every 2D and 3D figure has a list of mensuration formulas that establish a relationship amongst the different parameters. Let’s discuss the mensuration formulas of some shapes.
| Square | 4 × side |
| Rectangle | 2 × (length + width) |
| Parallelogram | 2 × (side1 + side2) |
| Triangle | side1 + side2 + side3 |
| Regular n-polygon | n × side |
| Trapezoid | height × (base1 + base2) / 2 |
| Trapezoid | base1 + base2 + height × [csc(theta1) + csc(theta2)] |
| Circle | 2 × pi × radius |
| Ellipse | 4 × radius1 × E(k,pi/2) E(k,pi/2) is the Complete Elliptic Integral of the Second Kind k = (1/radius1) × sqrt(radius12 – radius22) |
| Square | side2 |
| Rectangle | length × width |
| Parallelogram | base × height |
| Triangle | base × height / 2 |
| Regular n-polygon | (1/4) × n × side2 × cot(pi/n) |
| Trapezoid | height × (base1 + base2) / 2 |
| Circle | pi × radius2 |
| Ellipse | pi × radius1 × radius2 |
| Cube (surface) | 6 × side2 |
| Sphere (surface) | 4 × pi × radius2 |
| Cylinder (surface of side) | perimeter of circle × height |
| 2 × pi × radius × height | |
| Cylinder (whole surface) | Areas of top and bottom circles + Area of the side |
| 2(pi × radius2) + 2 × pi × radius × height | |
| Cone (surface) | pi × radius × side |
| Torus (surface) | pi2 × (radius22 – radius12) |
| Cube | side3 |
| Rectangular Prism | side1 × side2 × side3 |
| Sphere | (4/3) × pi × radius3 |
| Ellipsoid | (4/3) × pi × radius1 × radius2 × radius3 |
| Cylinder | pi × radius2 × height |
| Cone | (1/3) × pi × radius2 × height |
| Pyramid | (1/3) × (base area) × height |
| Torus | (1/4) × pi2 × (r1 + r2) × (r1 – r2)2 |
We hope that the above mentioned formulae would help you in preparing for the WBCS examination.
Best of Luck!!
Avision
Howrah, Liluah & Kolkata
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