Imagine the following situation: A farmer wants to find out how many meters of wire will be spent to fence a rectangular-shaped pasture plot. How should he proceed to reach a conclusion? In a very intuitive way, we concluded that he needs to determine the measurements of each side of the terrain and then add them up, obtaining how much would be spent. We call this procedure a perimeter.
Perimeter is the measure of the length of an outline or the sum of the measures of the sides of a flat figure.
The perimeter of a figure is represented by 2p.
Thus, the perimeter of the figure below will be:
2p = 10 cm + 9 cm + 10 cm + 9 cm = 38 cm
Example 1. Calculate the perimeter of the figure below:
Solution:
2p = 7 cm + 2 cm + 2 cm + 2 cm + 3 cm + 2 cm + 3 cm + 5 cm = 26 cm
Example 2. If the perimeter of a square is 64 cm, what is the measurement of each side of that square?
Solution: We know that the square is a quadrilateral with all sides congruent (with the same measure). Thus, to determine the measurement of each side we will have to divide the perimeter by 4.
Thus,
L = 64 ÷ 4 = 16 cm
Example 3. A farmer wants to enclose a rectangular plot of land 120 m long and 90 m wide. It is known that the fence will have 5 strands of wire. How many meters of wire will it take to make the fence? If a meter of wire costs R$15.00, what will be the total amount spent by the farmer?
Solution: Imagine that the fence will only have a strand of wire. The total amount of wire spent to get around the entire terrain will be equal to the perimeter measurement of the figure. As the fence will have 5 strands of wire, the total spent will be 5 times the value of the perimeter.
Perimeter calculation:
2p = 120m + 90m + 120m + 90m = 420m
Total spent wire:
5*420 = 2100 m of wire to make the fence.
As each meter of wire costs R$ 15.00, the total cost of the fence will be:
2100*15 = BRL 31. 500,00
By Marcelo Rigonatto
Specialist in Statistics and Mathematical Modeling
Brazil School Team
plane geometry - Math - Brazil School
Source: Brazil School - https://brasilescola.uol.com.br/matematica/perimetro-uma-forma-geometrica-plana.htm