Mensuration

Mensuration is a fundamental branch of mathematics that focuses on the measurement of geometric figures, their dimensions and their associated quantities. It plays a crucial role in various fields from construction and architecture to physics and engineering. In this chapter, we will explore the concepts of area, perimeter and volume and their real-world applications.

Perimeter

The total distance around the boundary of a shape is referred to as its perimeter. In mathematical notation, it is represented as 'P'.

Perimeter = Sum of all sides

The perimeter can be expressed using various units of measurement such as centimetres (cm), metres (m) and other units of length.

Area

Area is the quantity of space contained within a closed shape. In mathematical terms, it is denoted by the symbol 'A'.

The area can be expressed using various units of measurement such as square centimetres (cm²) and square metres (m²).

Steps for calculating the area of a figure using squared paper

a) Outline the shape by tracing it onto a square grid paper.
b) Disregard any areas that are smaller than half of a square.
c) If more than half of a square falls within the shape, count it as a whole square.
d) If exactly half of a square is within the shape, consider its area as ½ square unit. e) Add up all the counted squares and areas to find the total area of the given closed shape.

The figure shows the area of a figure using squared paper.

Volume and Surface Area

Volume is the amount of space that a solid object occupies. It is measured in units such as cubic centimetres (cm³) or cubic metres (m³).

Volume and Capacity are related terms:
Volume refers to the space taken up by an object.
Capacity refers to the amount that a container can hold.

Surface area is a measure of the total area that covers the outer part of a three-dimensional object. It includes all the exterior faces whether they are flat or curved. The surface area can be expressed as the same units of area such as square centimetres (cm²) and square metres (m²).