Mensuration: Definition and Meaning

Mensuration is a subsection of mathematics that studies the calculation of 2D and 3-dimensional geometric figures. It also examines their characteristics such as length, area, lateral surface area, and volume. Thus, mensuration refers to the field of geometry that is involved in determining lengths and volumes. It provides the basis for computation and explains the basic equations and properties of many figures and forms. Leonard Digges is the father of Mensuration, while Archimedes invented it.

Mensuration is a discipline of mathematics that is a means of measurement. We use mensuration in various circumstances throughout our lives.

Examples of Mensuration

Examples of mensuration include the measurement of length of fabric required for sewing, the size of a wall to be painted, the perimeter of the circular garden to be fenced, and the amount of water required to fill the tank. There are both standard and non-standard units of measurement that can measure objects or amounts.

What Tools Do We Require for Mensuration?

• Calliper: A tool used to measure the diameter.
• Try Square: A tool for determining flatness and squareness.
• Meter Stick: A measuring instrument with a length of one meter.
• Compass: A tool for drawing arcs and circles.

What Role do Mensuration and Computation Have in Our Daily Lives?

Measurement instruments make our lives easier and safer, as well as improve the quality and quantity of our lives. In addition, the capacity to properly quantify physical characteristics has arguably the greatest survival value, providing humans with an adaptive, evolutionary advantage refined through many years of natural selection.

Mensuration in Daily Life:

• A container's capacity is equal to its volume.
• The material volume in a hollow body is equal to the difference between the exterior and interior volumes.
• To calculate the cost of polishing/covering/painting a solid, first determine its exposed surface area and then multiply it by unit cost.

Essential Definitions

Plane figure: A figure with three or more sides or a circular border.

Perimeter: The entire length of a planar figure's sides.

Area: The amount of space occupied by a planar figure.

Surface area: The amount of space occupied by a solid's exterior surface.

Volume: The amount of space the solid takes up.

Solid figures: The items that occupy space and have three dimensions.

Fig 1 - Formulas to remember

Formulas:

• The area of the biggest triangle encircled by a semicircle of radius r is equal to r².
• If the area of a rectangle is A and the side ratio is a:b, then
  the first side = √A(a:b)
  second side = √A(b:a)
• The area of a square encircled by a circle of radius r is equal to 2r². √r is the side of a square encircled by a circle of radius r.
• If the area of a square is A, then the circumference of a circle created by the same perimeter is 4A/π.
• The number of diagonals in an n-sided regular polygon is given by (n-3)/2.