# Chapter 11 – Mensuration

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

Mensuration is an interesting topic in mathematics. It concerns the calculation of geometrical figures and forms such as the square, cuboid, cone, sphere, and cylinder, among others. Surface area, length, perimeter, and other properties may all be measured.

When it comes to measuring shapes and numbers, menstruation comes in handy. It works in all 2-D and 3-D geometric forms. We can solve mensuration problems quickly using a simple mensuration formula out of all other methods available. So, let’s look at these mensuration terms and formulas.

A 2-D form is enclosed by three or more straight lines on a plane surface. And such forms are only measured in length and width. A 3-D form, on the other hand, is described as one that is surrounded by a number of surfaces or planes. Depth, width, and duration are all present.

#### Concept of Measurement Using a Basic Unit

A basic unit of measurement is a quantifiable magnitude that makes the relationship between the item and the measurement clear to all.

People did not have any calculating instruments to quantify standard measurement units in the past. To solve this challenge, they devised a variety of creative methods to measure using the instruments at hand. They used the foot as a length indicator; for example, 1 foot is about 0.3 meters or 30 centimetres. A league was another duration measurement used by our forefathers. When we walked for an hour, one league equalled the distance travelled by a human. However, this device is no longer in operation.

To address the issue of disparate measuring systems (much like disparate languages), the International System of Units was created, and most industrialised and developing countries have embraced it. About the fact that this has been developed and implemented in major fields such as science and technology and government activities, most people still use their conventional or customary units.

#### Area and Perimeter

In mathematics, the two most significant properties of two-dimensional figures are area and perimeter. The perimeter of a form is described as the distance between its boundary and the area filled by it.

The region bounded by an object’s space is known as its area. The area of a shape is the space occupied by a figure or other geometric object. A shapes’ area is determined by its proportions and properties. There are various areas with different shapes.

The path or boundary around a shape is known as its perimeter. In a nutshell, it’s the measure of every shape as extended linearly. Based on their lengths, the perimeters of various shapes may be the same length.

#### What is the Definition of a Circle?

A circle is a closed, plane geometric form. It is a locus of a point rotating around a fixed point at a fixed distance away from the point in technical terms. It can also be seen as a closed curve with an outer line that is equidistant from the middle. The circumference of the circle is the defined distance from the origin. Many representations of the circle can be seen in everyday life, such as wheels, pizzas, a circular ground, and so on.

#### Area of a Circle

Consider a circle with a radius of r.

Then, A = πr^2 square units is the area of a circle.

#### Circumference of a circle

The circumference of a circle = 2πr,

where r is the radius of the circle;

π is the mathematical constant with a value of 3.14;

Pi (π) is a mathematical constant; it is the ratio of circumference and diameter of any circle.

C = π D

where C is the circumference of the circle;

D is the diameter of the circle.

#### The Perimeter of a Circle

The perimeter of a circle is the same as the circumference of a circle. Therefore, the formulas for the perimeter of a circle is

P = 2πR.

P = π D.

#### The Perimeter of a Semi-Circle

The semi-circle is formed when we divide the circle into two equal parts.

P = πr +2r.

#### Area of a Semi-circle

The area of the semi-circle is the region occupied by a semi-circle in a 2D plane.

A = πr2/2.

#### Conclusion

In this chapter, we learned about the basics of mensuration. We did a revision of the perimeter and idea of the circumference of a circle. We learned about the measurement units as well.

#### FAQs

1. In math, what is mensuration?
Mensuration is characterised in mathematics as the analysis of measuring various 2D and 3D geometric forms, including their surface areas, volumes, etc.
2. What is the difference between geometry and mensuration?
Mensuration is the analysis of the properties and relationships of points and lines of different forms. At the same time, geometry is concerned with the measurement of various parameters of shapes such as the perimeter, area, and length.
3. What is the difference between 2D and 3D mensuration?
The computation of different parameters, such as area and circumference of 2-dimensional forms such as squares, rectangles, circles, triangles, and so on, is known as 2D mensuration.
The analysis and measurement of a surface region, lateral surface area, and volume of 3-dimensional figures such as a square, sphere, cuboid, cone, cylinder, and so on is known as 3D mensuration.

4. What role does mensuration play in your life?
When it comes to the geometry of the universe, mensuration is a crucial subject. Mensuration, by extension, is the branch of geometry associated with determining distances, regions, and volumes.
5. What is the name of the father of mensuration?
The father of mensuration is Leonard Digges.

To learn more about mensuration through simple, interactive, and explanatory visualisations, try the MSVgo app. You’ll be able to watch this concept brought to life in videos along with real-life examples.

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