Introduction to Measuring Area

Overview

**Area of a plane figure** : The surface-span of a plane figure is the area of the surface. It is measured in square meter (or in one of other derived or similar forms).
Area is specified as a number in reference to the surface-span of a square of $1$ meter side.

surface-span

The length of a rod is the distance-span measured in meter.

For a surface of some shape (like a paper, or a leaf), the measure of the surface-span is area. *Area is the surface-span of an enclosed 2D-region.*

To specify distance-span or length, a reference-prototype-standard (ie a metal rod of specific material at specific temperature) was defined. Any length measurement is specified in reference to the prototype-standard.

Similarly, to specify area, a reference-prototype-standard can be defined. But, it is simpler to define the measurement of area using the already defined measure of length.

To specify the surface-span or area of a surface, a square of side $1$ meter is taken as the reference. The area of that is one square meter or $1{m}^{2}$. In the figure this is shown in the top right corner.

Area of a surface is given in reference to the area of a square of side $1$ meter. In the figure, the area of the given rectangle is the number of $1$ square meter squares fit in that rectangle. It is counted to $6$, so the area of the rectangle is $6{m}^{2}$.

The statement "area of the paper is $3$ square meter" specifies that "The surface-span of the paper equals $3$ surface-spans of a square of side $1$ meter".

summary

**Area of a plane figure** : The surface-span of a plane figure is the area of the surface. It is measured in square meter (or in one of other derived or similar forms).
Area is specified as a number in reference to the surface-span of a square of $1$ meter side.

Outline

The outline of material to learn "Mensuration basics : Length, Area, & Volume" is as follows.

Note: * click here for detailed outline of Mensuration (Basics). *

• ** Measuring Basics**

→ __Introduction to Standards__

→ __Measuring Length__

→ __Accurate & Approximate Meaures__

→ __Measuring Area__

→ __Measuring Volume__

→ __Conversion between Units of Measure__

• ** 2D shapes**

→ __Perimeter of Polygons__

→ __Area of Square & rectangle__

→ __Area of Triangle__

→ __Area of Polygons__

→ __Perimeter and area of a Circle__

→ __Perimeter & Area of Quadrilaterals__

• ** 3D shapes**

→ __Surface Area of Cube, Cuboid, Cylinder__

→ __Volume of Cube, Cuboid, Cylinder__