Have you ever thought how much parking space does your car need? Or what dimension bed can fit in your room? The answer to these questions lies in mensuration formulas. In Latin, mensuration means measurement. Hence, mensuration is that branch of mathematics which deals with the calculation of length, area and volume of both 2D and 3D geometric shapes. While a 2D shape has only two dimensions i.e. length and breadth, a 3D figure has length, breadth and height. Area(A) and Perimeter(P) are the two common parameters we measure for 2D shapes. For 3D, Volume(V), total, lateral and curved surface area is calculated. But why do you need to learn these formulas now? Quantitative reasoning section of exams like GRE, GMAT, SSC, RBI-Grade B etc. is considered as one of the toughest yet highly scoring section. Thus, speed and accuracy plays a pivotal role in scoring well. Now here comes the role of memorizing mensuration formulas. If you can recall a formula, then you can invest more time on other questions. Here is a blog that compiles all the relevant mensuration formulas for competitive exams.
Introduction to Mensuration Formulas – Important Terms
Before we get down to the nitty-gritties of the mensuration formulas, let us recall some important terms:
- Area (A) : It is the surface enclosed by a given shape. The S.I. Units to denote area are m2/cm2.
- Perimeter (P) : It is simply the boundary length of an area and the units used are cm/m.
- Volume (V) : The space occupied by a solid or a 3-Dimensional object is called volume. The units are cm3/m3.
- Curved Surface Area (CSA): It is the area enclosed by the curved portion of a geometrical object. its units are m2/cm2.
- Diagonal (d) : A line that joins two vertices of a geometrical figure is called a diagonal.
- Total Surface Area (TSA) : The sum total of areas of all the surfaces of an object is called TSA. m2/cm2 are its S.I. units.
- Lateral Surface Area (LSA) : Sum total of areas of all surfaces except top and the base of an object is called LSA. It is represented by m2/cm2 .
The major 2D figures are square, triangle, rectangle, circle, rhombus and parallelograms. Let us now have a look at the mensuration formulas of all the important 2D geometrical figures:
|Square||a2||4a||√2a||Side = a|
|Rectangle||lb||2(l+b)||√2 (l2+b2)||Length = l, Breadth = b|
|Rhombus||1/2 d1d2||4a||2A/d2||Diagonals = d1 and d2|
|Parallelogram||ph||2(p+q)||p2+q2-2pqcosβ||Base = pSide = qAngle = β|
|Circle||πr2||2πr||–||Radius = r|
Let us have a look at the different types of triangles and their respective mensuration formulas:
- The triangle in which neither of the three sides and angles are of the same value is called a Scalene triangle. In this, the sum total of all the angles equals 180 degrees.
- An isosceles triangle is the one in which any of the 2 sides are equal and the values of 2 angles are also equal.
- The triangle whose all sides are equal is called an Equilateral triangle. Here, the value of all the 3 angles is 60 degrees.
- A triangle in which one angle equals 90 degrees is called a Right angled Triangle. The side in this triangle is calculated using Pythagoras theorem.
|Scalene||(bh)/2||a+b+c||Sides = a,b,cHeight = h|
|Isosceles||1/2bh S(S-a)(S-b)(S-c)*||2a+b||Semi-perimeter = S|
|Equilateral||a23/4||3a||Side = a|
*If sides are mentioned then area of a scalene triangle is calculated using Heron’s formula where S=(a+b+c)/2
Below is a compilation of mensuration formulas of all the important 3D geometrical figures:
|Shapes||Volume||Curved Surface Area/Lateral Surface Area||Total Surface Area||Nomenclature|
|Sphere||4/3 πr3||4 πr2||4πr2||Radius = r|
|Cube||a3||4a2||6a2||Side = a|
|Cuboid||lbh||2h(l+b)||2(lb+bh+hl)||Length = l, Breadth = b, height = h|
|Cylinder||πr2h||2πrh||2πr(r+h)||Radius of base = r|
|Cone||1/3 πr2h||πrl||πr(s+l)||Slant height = s|
Thus, we have provided you with a list of all the relevant mensuration formulas for competitive examinations. If you want any guidance on how to score well in these exams, you can contact mentors and counselors at Leverage Edu.