Introduction to Mensuration

Mensuration is a branch of mathematics concerned with the measuring of 2D and 3D figures based on factors such as length, volume, shape, surface area, and so on. To put it another way, it is a method of measuring based on algebraic equations and mathematical formulas. Let’s take a closer look at the notion of mensuration, the formulas, and some instances to help us grasp it better.

Mensuration is defined as the act of measuring something. The world we live in is three-dimensional. In both primary and secondary school mathematics, the concept of measuring is crucial. Furthermore, measuring has a direct impact on our daily life. We learn to measure objects in both 3D and 2D shapes as we learn to measure them. Both standard and nonstandard units of measurement can be used to measure objects or quantities.

Hand spans, for example, are a non-standard unit for measuring length. You can even make an activity out of it by having youngsters use Hand spans to measure the length of things. Allow youngsters to observe that there is always the possibility of a discrepancy when measuring objects with non-standard units. As a result, fixed units of measurement were needed. We now use units like kilometre, metre, kilo-gramme, gramme, litre, millilitre, and millilitre to measure length, weight, and capacity.

Definition of 3D Shapes:

A three-dimensional shape with faces, edges, and vertices is referred to as a 3D shape. They have a total surface area that encompasses all of their faces. The volume of these shapes is determined by the amount of space they occupy. Cube, cuboid, cone, and cylinder are examples of 3D shapes, while real-world examples include a book, a party hat, and a coke tin.

Definition of 2D Shapes:

2D shapes are figures with 2 dimension length and breadth and no height. There is no thickness to them, and they can only be measured in two dimensions.

Important Measuring Terminology:

Mensuration is the science of measuring planar and solid shapes. Let’s have a look at some of the key terms:

Terms:

A 2-dimensional figure’s area is the amount of space it requires. It’s calculated in square units.A 3D shape’s volume is the amount of space it takes up. It’s measured in cubic meters.

Perimeter: The complete distance around the form or the length of any closed shape’s boundary is referred to as the perimeter. It’s calculated in square units.

Surface Area: The total area filled by the surfaces of a 3D object is known as Surface Area. Curved or Lateral Surface Area and Total Surface Area are the two types of surface area.

Formulas for Measuring:

Both 3D and 2D shapes are used in mensuration formulas. The surface area and volume of these forms are the most widely used formulas. But first, let’s go through some of the formulas for these forms.

Formulas:

Sphere

Diameter = 2 × r; (where ‘r’ is the radius)

Surface Area = 4πr²

Volume = (4/3)πr³

Cylinder

Total Surface Area = 2πr(h+r); (where ‘r’ is the radius and ‘h’ is the height of the cylinder)

Volume = πr²h

Cone

Curved Surface Area = πrl; (where ‘l’ is the slant height and l = √(h² + r²))

Total Surface Area = πr(l + r)

Volume = (1/3)πr²h

Cube

Lateral Surface Area = 4a²; (where ‘a’ is the side length of the cube)

Total Surface Area = 6a²

Volume = a³

Cuboid

Lateral Surface Area = 2h(l + w); (where ‘h’ is the height, ‘l’ is the length and ‘w’ is the width)

Total Surface Area = 2 (lw + wh + lh)

Volume = (l × w × h)

Prism

Surface Area = [(2 × Base Area) + (Perimeter × Height)]

Volume = (Base Area × Height)

Pyramid

Surface Area = Base Area + (1/2 × Perimeter × Slant Height)

Volume = [(1/3) × Base Area × Altitude]

Conclusion:

Mensuration is a branch of mathematics that deals with the computation of 2D and 3D geometric figures. It also works with dimensions like length, area, lateral surface area, and volume. As a result,mensuration deals with the branch of geometry concerned with determining lengths and volumes.It explains the basic equations and properties of different shapes and figures that serves as a foundation for calculation. Mensuration is a mathematical term in geometry that helps in calculating area and volume.