Here’s what mensuration is in mathematics. We can define mensuration as the branch of mathematics that studies the measurement of various different geometric figures and their parameters like length, volume, shape, surface area, lateral surface area, etc. Here, the concepts of mensuration are explained and all the important mensuration formulas and properties of different geometric shapes and figures are covered.
Mensuration Maths – Definition
Now we know where mensuration can be used in mathematics. Mensuration can be defined as the branch of mathematics which deals with the length, volume or area of different geometric shapes. These shapes exist in 2 dimensions or 3 dimensions. Let’s learn the difference between the two.
Difference Between 2D and 3D shapes
2D shape |
3D shape |
If any shape is surrounded by three or more straight lines in a plane, then it is known as a 2D shape. |
If any shape is surrounded by a no. of surfaces or planes then it is known to be a 3D shape. |
These 2D shapes have no height or depth. |
These 3D shapes are also known as solid shapes and unlike 2D shapes they have both height or depth. |
We can measure the area and perimeter of 2D shapes. |
We can measure their volume, CSA, LSA or TSA of 3D shapes. |
Mensuration in Maths – Important Terminologies
Let’s learn a few more definitions related to this topic.
Terms |
Abbreviation |
Unit |
Definition |
Area |
A |
m2 or cm2 |
The area is the surface which is covered by the closed shape. |
Perimeter |
P |
m or cm |
Perimeter can be defined as the measure of the continuous line along the boundary of the given figure. |
Volume |
V |
m3 or cm3 |
In a 3D shape, the space occupied by object is known as the Volume. |
Curved Surface Area |
CSA |
m2 or cm2 |
If there’s a curved surface, then the total area is called a Curved Surface area. Example: Sphere or Cylinder. |
Lateral Surface area |
LSA |
m2 or cm2 |
The total area of all the lateral surfaces that surrounds the figure is called the Lateral Surface area. |
Total Surface Area |
TSA |
m2 or cm2 |
If there are many surfaces like in 3D figures, then the sum of the area of all these surfaces in a closed shape is called Total Surface area. |
Square Unit |
– |
m2 or cm2 |
The area covered by a square of side one unit is known as a Square unit. |
Cube Unit |
– |
m3 or cm3 |
The volume occupied by a cube having a side equivalent to one unit. |
Mensuration is a measurement system
Measuring can be understood as mensuration. There are three dimensions to the world. Primary as well as secondary school mathematics emphasize measurement as an essential concept. In addition, measurement is fundamental to our lives on a daily basis. It is important to learn how to measure 3D and 2D objects when learning how to measure. Mensuration is the study of figuring out lengths, volumes, shapes, surface areas, and other parameters on 2D and 3D figures.
Standard and nonstandard units of measurement can both be used for measuring objects or quantities. Rather than a standard measurement unit, handspans might be considered a non-standard unit. There are even activities you can do with it. One would be for children to make measurements using their hand spans. Make sure children know that there will always be a chance of a discrepancy when measuring objects with non-standard units. Standard measurements prevent this from happening. There are more units available for estimating parameters like length, weight, and capacity, like kilometres, metres, kilograms, grams, litres, millilitres, etc.
Measurement and Mensuration-Related Topics
Following are two images depicting all the concepts of mensuration in relation to these two images. Physicists and product designers can also find connections between these concepts. A child needs the basic skills of operating on quantities, understanding lines, and understanding angles if he/she is to be proficient at these concepts.
Mathematical Formula for Mensuration
Here are the important math formulas for mensuration.
1. Square
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Area of Square: Formula for Area of square (A) = a2 , where A = Area of a square, a = Side of a square
Perimeter of Square: Formula for Perimeter of a Square (P) = 4 × a , where P = Perimeter of a square , a = Side of square
2. Rectangle
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Perimeter of the Rectangle: P= 2 × ( L+B) , where P = Perimeter of a rectangle, L = Length of a rectangle , B= Breadth of a rectangle
Area of the Rectangle: A= L× B , where A = Area of a rectangle, L = Length of a rectangle , B= Breadth of a rectangle
3. Cube
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Surface area of a cube: S = 6 × A2 , where S= Area of a rectangle, A= Length of the side of the cube
Volume of a cube: V =A3 where, V = Volume of the cube, A = Side of the cube
4. Cuboid
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Surface Area of a Cuboid: S = 2 × (LB + BH + HL) ,where S = Surface Area of a cuboid, L = Length of cuboid, B= Breadth of the cuboid , H = Height of the cuboid
Volume of Cuboid: V = L × B × H, where V = Volume of the cuboid, L= Length of the cuboid, H equals the height of the cuboid and B = Breadth of the cuboid .
5. Cylinder
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Surface Area of a Cylinder: S= 2 × π × R × (R+H), where S= Surface Area of the Cylinder, R = Radius of the Cylinder, H =Height of the cylinder
Volume of a Cylinder: V= π × R2 × H, where V = Volume of the Cylinder, R = Radius of the Cylinder, H =Height of the cylinder
6. Sphere
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Surface Area of a Sphere: S =4 × π × R2 , where S= Surface Area of the sphere, R = Radius of the Sphere
Volume of a Sphere: V = 4/3 × π × R3, where V= Volume of the sphere, R = Radius of the Sphere
7. Cone
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Surface Area of a Right circular cone: S = π × r(l+r) , where S= Surface Area of the Right Circular Cone, l = Length of the cone, r = Radius of the cone
Volume of a Right circular cone: V = ( π × R2 × H ) ÷ 3, where V = Volume of the Right circular cone , H = Height of the cone.
Questions To Be Solved
Question 1. What is the area and perimeter of a square with a side of 4 cm?
Solution: We know the formula to find the area of a square and perimeter of a square,
Area of square (A) = a2 , Here the value of a = 4 cm
Therefore, the Area of a square = 42 = 16 cm
Perimeter of square = 4 × a , We know that the value of a = 4 cm
Therefore, the Perimeter of a square = 4 × 4 = 16 cm
Question 2. How do you calculate Mensuration? What is Mensuration?
Solution: Mensuration Formulas;
-
Area of rectangle (A) is equal to length(l) × Breath(b)
-
Perimeter of a rectangle (P) is equal to 2 × (Length(l) + Breath(b))
-
Area of a square (A) is equal to Length (l) × Length (l)
-
Perimeter of a square (P) is equal to 4 × Length (l)
-
Area of a parallelogram (A) is equal to Length(l) × Height(h)
-
Perimeter of a parallelogram (P) is equal to 2 × (length(l) + Breadth(b))
Now we know what is mensuration in mathematics. Here’s the definition of mensuration and we can define mensuration as the branch of mathematics which deals with the study of different geometrical shapes,their areas, and Volume. In simple words, it is all about the process of measurement.
Question 3. How many types of Mensuration are there? Which topics come under Mensuration? What is the volume in Mensuration?
Solution: Types of Mensuration; There are two types of Mensuration: 2D Mensuration and 3D Mensuration.
So let us study the topics that come under mensuration:
Here are the Volume Formulas: We know that solid occupies some regions in space and the magnitude of this region is known as the Volume of the solid. One of the standard units of volume is cubic centimeter (cm3) .
Conclusion
Mensuration is one of the most important topics in modern mathematics. Calculation of Areas and Volumes can be fun. Having a three dimensional figure and being able to dissect its ongoing mathematically is an interesting endeavor. You can also download the study material for free from the website. Guess what! You have stumbled upon the absolute best place to find answers to your questions.