Area and perimeter of a circumference

Area

The curve called circumference contains a surface. This surface is called the area of the circumference.

There is a very simple formula that allows us to calculate the area enclosed within the circumference just by knowing the length of the radius of the circle.

Let us call $r$ the radius of the circle, then the area of the circle is:

$$A=\pi \cdot r^2$$

Remember that $\pi$ is an irrational number, so if we want to express the result of the area without the constant $\pi$, we have to calculate it using the approximation $\pi =3,1416$

Let's see an example of how we calculate the area of a circle.

Note 1: we can see that the units of the parameter $r$ are cm. It could be any unit of measurement, such as cm, m, mm... or other units such as inches or miles, for example.

Note 2: the area units are units of squared length because we have multiplied a distance by itself.

Perimeter

Consider a circumference, the perimeter of a circle is the length of the curve; in other words, it is the distance that a person would walk if he started walking from any point on the circumference and gave a whole lap around the circumference until arriving at the point of departure.

In a similar way as with the area, there is an expression that allows us to know the length (or perimeter) of the circumference simply by knowing its radius $r$.

The expression is:

$$P=2\cdot \pi \cdot r$$

Let's see it more clearly with an example.