Have you ever thought about how much parking space your car needs? 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 that deals with the calculation of the length, area, and volume of both 2D and 3D geometric shapes. 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 play 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.
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What is Mensuration?
Mensuration is a prominent concept of Mathematics and studies the measurement of different geometric shapes and figures. As discussed, mensuration formulas come handy in scores of competitive exams. It helps us understand the dimensions of various 2-dimensional and 3-dimensional objects. 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.
Difference Between 2D & 3D Shapes
Before diving it mensuration formulas, it is important to understand the two major types of geometric shapes, i.e. Two-dimensional (2D) and three-dimensional (3D).
|2D Shapes||3D Shapes|
|A 2D shape refers to a figure which is surrounded by three or multiple straight lines in a plane.||A 3D shape is a figure covered by multiple surfaces or planes.|
|2D shapes do not contain any depth or height.||3D shapes are solid shapes and have depth as well as height.|
|They comprise 2D length and breadth.||They consist of length, breadth and width as they are three-dimension.|
|Area and perimeter of these shapes are measured.||Volume, CSA, LSA and TSA is measured for these shapes.|
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Mensuration Formulas: Important Terms
Before we get down to the nitty-gritty of the mensuration formulas, let us recall some important terms:
|Area (A)||It is the surface enclosed by a given shape.||m2 or cm2|
|Perimeter (P)||It is simply the boundary length of an area.||m or cm|
|Volume (V)||The space occupied by a solid or |
a 3-Dimensional object is called volume.
|cm3 or m3|
|Curved Surface Area (CSA)||It is the area enclosed by the curved portion |
of a geometrical object.
|m2 or cm2|
|Total Surface Area (TSA)||The sum total of areas of all the surfaces |
of an object is called TSA.
|Lateral Surface Area (LSA)||Sum total of areas of all surfaces except |
the top and the base of an object is called LSA.
|Diagonal (d)||A line that joins two vertices of a geometrical |
figure is called a diagonal.
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Mensuration Formulas for 2D Shapes
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:
|a2||4a||√2a||Side = a|
|l x b||2(l+b)||√2 (l2+b2)||Length = lBreadth = b|
|½ × d1 × d2||4a||2A/d2||Diagonals = d1 and d2|
|p x h||2(p+q)||√(p2+q2-2pqcosβ)||Base = pSide = qAngle = β|
|–||Radius = r|
Types of Triangles
Triangles are another important 2D shapes whose formulas are important to memorize. But before we delve into the mensuration formulas of these objects, let us first understand their types.
- 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 the Pythagoras theorem.
Now that you are familiar with different types of triangles, here are the mensuration formulas for Scalene, Right-Angled, Isosceles, and Equilateral triangles:
|Scalene||(bh)/2||a+b+c||Sides = a,b,c|
Height = h
|Isosceles||1/2 x b x h|
|2a+b||Semi-perimeter = S|
|Equilateral||a2 x √3/4||3a||Side = a|
*If sides are mentioned then the area of a scalene triangle is calculated using Heron’s formula where S=(a+b+c)/2
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3D Figures Mensuration Formulas
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||4 x a2||6a2||Side = a|
|Cuboid||l x b x h||2h(l+b)||2(lb+bh+hl)||Length = l|
Breadth = b
height = h
|Cylinder||πr2 x h||2πrh||2πr(r+h)||Radius of base = r|
|Cone||1/3πr2h||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.