Let’s Learn About Mensuration and Its Applications!
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
Mensuration in Maths - Important Terminologies
Let’s learn a few more definitions related to this topic.
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:
Cylinder.
Circles.
Polygons.
Rectangles and Squares
Trapezium, Parallelogram and Rhombus.
Area and Perimeter.
Cube and Cuboid.
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) .
Cylinder; V = πr2h
Sphere; V = 4/3 πr3
Cube;V = a3
Cuboid; V = L*B*H
Hemisphere; V = (⅔) πr3
Cone; V = (⅓) πr2h
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.
FAQs on Mensuration Formula
1.The importance of mensuration terminologies?
Mensuration Terminologies: An Overview
The following terms are used to describe mensuration;
Perimeter:
The perimeter of a geometric figure can be considered the continuous length of its sides.The figure is surrounded by a boundary. It can be measured in several ways. The length, width, and height of things are measured in millimetres, centimetres, inches, etc.
Area:
Geographic figures are measured by their area or region they occupy. These are units of measurement.
The area of a square is measured by a square unit
The dimensions of a square meter are m2, cm2, km2.
Lateral Surface Area:
A geometrical figure's lateral surface area is the lateral surface area (LSA) that is covered by
An illustration of the lateral lines.
Surfaces that are Curved:
The surface area of a curvilinear geometric figure is defined as the region that lies within its curvature the curves are covered.
This Surface has the Following Area:
It is also known as the overall surface area/ total surface area (TSA), which refers to the area or region covered by the figure in its entirety.
Volume:
There are three dimensions in three-dimensional figures, therefore the space occupied by a three dimensional object is known as volume. the space is measured in cubic units for example cubic meter, cubic kilometre, cubic hectare, and so forth.
2. Describe how mensuration is used in daily life?
Measuring is used in real life in a wide variety of ways. Below are a few examples:
Fields and sites are measured for the purpose of purchasing/selling them.
For packing solid foods, milk, and liquids, the volume of each item should be measured.
Estimating the cost of painting a house, etc., by measuring the surface area.
3. What are the differences between mensuration and geometry?
The difference between mensuration and geometry can be summarised as follows:
Geometry looks at points and lines and their properties and relations, whereas mensuration refers to the measurement of parameters of geometrical shapes, such as their perimeter, area, and volume. The difference between mensuration and geometry is that mensuration is the branch of mathematics that deals with measurement, such as the articulation and application of algebraic formulae to the measurement of areas, volumes, and other parameters of geometric figures, whereas geometry is (in mathematics) the branch of mathematics that deals with spatial relationships.