Mensuration

Mensuration is defined as the act of measuring something. The world we live in is three-dimensional. In both primary and high 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. Handspans, for example, are a non-standard unit for measuring length.

Mensuration’s Applications:

Mensuration is an essential issue with a wide range of applications in real-world situations:-

1. Agricultural field measurements and floor areas are essential for purchase/sale transactions.
2. Volumes necessary for packaging milk, liquids, and solid edible food items are measured.
3. Surface area measurements are essential for estimating the cost of painting houses, buildings, and other structures.
4. Water levels and amounts in rivers and lakes can be determined using volumes and heights.
5. Optimum cost packaging sachets for milk and other products, such as tetra packaging.

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, and real-world examples include a book, a party hat, and a coke tin.

Definition of 2D Shapes

2D shapes are plane figures that are fully flat and have only two dimensions – length and width – in geometry. There is no thickness to them, and they can only be measured in two dimensions.

List of formulas:

Here’s a quick rundown of mensuration formulas that are often used to address solid and planar figure problems.

Trapezium Area= Height* (sum of parallel sides)/2 

Rhombus Area = ½*( d1 * d2); where d1 and d2 are the rhombus’ two diagonals.

The area of a Special Quadrilateral is equal to 1/2 * d * (h1 + h2), where d is the diagonal and h1 and h2are the perpendiculars taken from the vertices on the diagonals.

Cuboid surface area = 2(lb* bh * hl); where l, b, and h are the cuboid’s length, width, and height.

Cube surface area = 6a2, where a denotes the cube’s side.

The surface area of a cylinder is equal to 2πr(r + h), where h is the height and r is the radius of the cylinder.

Cuboid Volume = l * b* h, where l, b, and h are the cuboid’s length, width, and height, respectively.

Cube Volume = a3; where a denotes the cube’s side.

The volume of a cylinder is equal to πr2h, where h is the height and r is the radius of the cylinder.

Applications of formula in day to day life:

In our surroundings, we are surrounded by a variety of shapes and figures. We come into scenarios where we need to compute the area, perimeter, and volume of forms on a regular basis. Let’s look at how mensuration formulas are used in practice.

• The measuring of agricultural fields and floor spaces required for purchase/sale transactions is done using mensuration formulas.
• The perimeter formulas can be used to compute the length of plot and field boundaries.
• The formulas for volume can be used to measure liquids such as packaged milk, oil, or solid edible food products.
• Mensuration formulas can be used to determine the volumes and heights needed to determine the levels and amounts of water in rivers and lakes.
• The cost of painting houses, buildings, and other structures can be estimated using the surface area formulas in mensuration.

Conclusion:

The branch of mathematics that deals with measuring is known as mensuration. It was first used in Egypt for land surveying and other civil engineering projects. Archimedes is known as the “Father of Measurement.” Mensuration is a discipline of mathematics that studies the measurements of various geometrical forms and their areas, perimeters, and volumes, among other things. Mensuration describes a variety of geometrical shapes, such as two-dimensional shapes, as well as their attributes and formulas. Mensuration can be applied to both two- and three-dimensional shapes.