perimeter

We explain what a perimeter is, how it is calculated in different geometric figures and its applications in other disciplines.

The concept of perimeter is necessary to advance towards algebra and trigonometry.

What is the perimeter?

In geometry, the perimeter is the sum of the lengths from the sides of any geometric figure flat. It is a key concept for math, which together with the area, which is close to him, is necessary to master in order to move towards more advanced mathematics such as algebra and the trigonometry, since they allow the construction of polygons.

The word perimeter comes from ancient Greek (union of voices peri, "everything and metron, “Measure”), since the ancient Greek philosophers were the first to calculate it. The first thought of this type is attributed to the philosopher Archimedes (c. 287-212 BC).

The concept applies both to distance and length, or to the contour of figures; but in the case of circles it is renamed circumference. Half of the perimeter is called the semi-perimeter. The perimeter is represented by the letter P.

Practical applications of the perimeter

A fence marks the perimeter of a garden.

The calculation of the perimeter has many practical applications, especially for the work of architecture, engineering and construction. For example, it can be used to calculate the edges or boundary of a space or an object, such as a piece of land or a building.

If we want, for example, to place a fence around our garden, it will be necessary to calculate the perimeter of its surface, to know how many materials to buy and how to place them.

Perimeter of a circle

To calculate the perimeter of a circle, you have to know its radius or its diameter.

The perimeter of a circle is called the circumference, and it 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 radius of the circle and d is the length of the diameter of the circle. In the case of a semicircle, the formula will change to:

P = 2r + r. π = r (2 + π)

Perimeter of a rectangle

The perimeter of a rectangle is easy to calculate.

In the case of a rectangle, you do not need to calculate the perimeter more than adding the lengths of its two long sides and its two short sides. That is, if the rectangle has two sides a (a1, a2) and two sides b (b1, b2), the perimeter will be calculated by adding a1 + a2 + b1 + b2.

Perimeter of a square

The sides of a square are equal to each other, as are the sides of a right triangle.

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), it will suffice to 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.
  • Triangle equilateral. 3 identical sides that measure b, hence P = b x 3.

The same applies to other similar figures, regardless of their number of sides. On the other hand, for isosceles and scalene triangles, each length of each side must be added.

Perimeter of an irregular polygon

To calculate the perimeter of an irregular polygon, you must know the length of its sides.

In the case of irregular polygons, that is, those that do not have sides and angles identical, it will suffice to add the measures of all the sides of the polygon, regardless of their shape. In case we do not have the measurements of some of these sides, the task will be complicated because we must first calculate them, but then we can proceed to add them without any difficulty.

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