We explain what a perimeter is, how it is calculated in different geometric figures, and its applications in other disciplines.
What is perimeter?
In geometry, perimeter is the sum of the lengths of the sides of any plane geometric figure. It is a key concept for mathematics, which, along with the closely related concept of area, is necessary to master in order to move on to more advanced mathematics such as algebra and trigonometry, as they allow the construction of polygons.
The word perimeter comes from ancient Greek (a combination of the words peri, “whole,” and metron, “measure”), as the ancient Greek philosophers were the first to calculate it. The first such idea is attributed to the philosopher Archimedes (c. 287–212 BC). You must read about Triangle once.
The concept applies to both distance and length, or to the outline of figures; but in the case of circles, it is called the circumference. Half the perimeter is called the semiperimeter. The perimeter is represented by the letter P.
Practical Applications of Perimeter
Calculating perimeter has numerous practical applications, especially for architecture, engineering, and construction. For example, it can be used to calculate the edges or boundaries of a space or object, such as land or a building.
If we want, for example, to build a fence around our garden, we will need to calculate the perimeter of its surface to know how much material to buy and how to place it.
Perimeter of a Circle
The perimeter of a circle is called the circumference and is calculated by applying the following formula:
P = 2π . r = dπ
Where π is the mathematical constant equivalent to 3.14159…, r is the length of the circle’s radius, and d is the length of its diameter. In the case of a semicircle, the formula changes to:
P = 2r + r . π = r(2 + π)
Perimeter of a Rectangle
In the case of a rectangle, the perimeter is calculated by simply adding the lengths of its two long sides and its two short sides. That is, if the rectangle has two a sides (a1, a2) and two b sides (b1, b2), the perimeter is calculated by adding a1 + a2 + b1 + b2. Maybe you should definitely read about Polyhedra once.
Perimeter of a Square
The case of squares is identical to that of rectangles. In fact, in the case of regular polygons, whose sides measure exactly the same (such as equilateral triangles), simply multiply the length of one side by the number of sides in the figure:
- Square: 4 identical sides measuring a, therefore, P = a x 4.
- Equilateral Triangle: 3 identical sides measuring b, therefore, P = b x 3.
The same applies to other similar figures, regardless of their number of sides. However, for isosceles and scalene triangles, the length of each side must be added together.
Perimeter of an Irregular Polygon
In the case of irregular polygons, that is, those that do not have identical sides and angles, simply add the measurements of all the sides of the polygon, regardless of its shape. If we don’t have the measurements of some of these sides, the task will be more complicated because we will have to calculate them first, but then we can add them together without any difficulty.
References
All the information we offer is supported by authoritative and up-to-date bibliographic sources, ensuring reliable content in line with our editorial principles.
- “Perimeter” on Wikipedia.
- “What are perimeters and areas?” (video) on Aula365.
- “Perimeter and area” on Monterrey Institute.
- “Calculating the area and perimeter” on Math Planet.
- “Introduction to perimeter” (video) on Khan Academy.
