Area and Perimeter are two of the fundamental concepts in the field of mathematics. Both concepts are used to measure the physical space occupied by objects and their measurements.

**Area vs Perimeter**

The difference between Area and Perimeter is that the area is the space inside a particular shape or object while the perimeter is the outside distance around a certain object.

The area is defined as the space occupied by a flat two-dimensional object. While the perimeter of an object is the total length of its sides or boundaries.

The area is always measured by the number of square units that fit into a particular shape or object and hence is measured in square units, while the perimeter measures length and is measured in units like feet, inches, meters, etc.

## Comparison Table Between Area and Perimeter (in Tabular Form)

Parameter of Comparison | Area | Perimeter |
---|---|---|

Definition | The area is the space covered or occupied by a two-dimensional object or shape. | The perimeter of a closed object is the distance around it. |

Dimensions | The area is used to find the space taken by two-dimensional objects. | Perimeter is used to find the sides of a one- dimensional object or shape. |

How to find | It is found by measuring the number of squares that can fit into that particular shape or figure. | It is found by adding the length of all sides of a closed figure. |

Unit of measurement | The unit of measurement for the area is in square units. For example cm2, m2, km2, etc. | The unit of measurement for the perimeter of an object is in the normal or linear unit of length. For example a+b+c or sum of all sides of the object. |

Indication | The area indicates the space covered by a figure. | Perimeter indicates the boundary or rim of the particular object. |

## What is Area?

In the field of geometry, area refers to the space that is covered or occupied by any flat shape or object. The word ‘area’ is derived from the Latin word, ‘area’ which means any vacant piece of ground.

The area also means the particular amount of space that can be held within closed boundaries. Usually, the area is found out for two-dimensional figures like square and rectangle. While there are not only two- dimensional but also three- dimensional figures whose area needs to be found out.

The area of these three- dimensional figures is called as Surface Area. Many figures aren’t as simple as a square, rectangle, or a triangle, in these cases, the area of theses composite figures is found out by adding the areas of the simple figures that form these composite ones.

The standard unit of area in the International System of units is square meters, written as m^{2}, where m is the length of one side of the object. Areas of simple figures like circle, square, or triangle can be found out using well-known common formulas.

While, for polygons, the area can be found out by dividing them into respective triangles and then adding the areas of all of them. Algebraically. The area is considered to be the square of the corresponding unit of length, and hence could be in square meters (m^{2}), square centimeters (cm^{2}), square millimeters (mm^{2}), square kilometers (km^{2}), square yards (yd^{2}) or even square miles (mm^{2}).

Some of the basic formulas used to find area are as follows:

- Square: a
^{ 2} - Rectangle: ab
- Parallelogram: bh
- Trapezoid: h/2 (b
_{1}+ b_{2}) - Circle: πr²
- Triangle: ½ bh

In real life, the area can be calculated to know how much carpet is to be used to cover the floor or even to determine how much area is to be painted on a curtain wall.

## What is Perimeter?

The distance around a particular shape is known as its perimeter. It is the length of the boundary of any shape or one-dimensional or even two- dimensional object.

The word finds its derivative from the Greek words ‘peri’ which means around and ‘metron’ meaning measure. It is calculated by adding the lengths of all sides of the closed figure. The term used to indicate the boundaries of a figure is usually known as its perimeter, while in case of a circle it is known as its circumference.

In the customary units of measurements, perimeter or the total length is measured by these commons units like an inch, yards, foot, or miles. While in the metric system of measurement the units of length could be millimeters, centimeters, meters, and kilometers.

Some of the basic formulas used to find area are as follows:

- Square: 4a
- Rectangle: 2(length + width)
- Parallelogram: 2(base + height)
- Triangle: a + b + c
- Trapezoid: a + b + c + d
- Kite: 2a + 2b
- Hexagon: 6a

In real life, the perimeter is calculated to find the length of the boundary to be fenced or to find the length of a ribbon required.

**Main Differences Between Area and Perimeter**

- Area refers to the space covered or occupied by an object while Perimeter refers to the length of the boundary of the same object.
**The main difference between Area and Perimeter is that**area measures two dimensions of an object, i.e. Length and Width, while Perimeter measures only one dimension, i.e. the length of the object.- The measuring unit for Area is in square meters while the units used for measuring perimeter is the normal units used for lengths.
- In simpler terms area can be described as a concept that deals with the inside of a figure while Perimeter is something that is concerned with the borders or outside of a figure.
- The area might be needed to be found out how much area needs to be carpeted on a floor, while the perimeter is required when you need to know how much length of wire you require to fence your field.

## Conclusion

Both theses mathematical concepts are closely related and are used in geometrical as well as algebraic calculations. While the area talks about the space or extent of the surface covered, perimeter talks of the continuous line that that forms a closed figure.

It is easier to find out one using the other. It is also possible that figures that have similar areas have different perimeters and those with different perimeters have the same area.

## References

- https://www.splashlearn.com/math-vocabulary/geometry/perimeter
- https://www.splashlearn.com/math-vocabulary/geometry/area

Table of Contents

Ahmed AliFrom my childhood days, I remember the use of Hero’s formula to calculate the area of a triangle.