Example of How to Find the Area of ​​the Circle

We call a circle the figure that is formed by the circumference and the area of ​​the plane that is limited by it. Furthermore, the segment that joins the center of the circle with any point belonging to the circumference is called the "Radius" of the circumference.
We can consider the circle as if it were a regular polygon with infinite sides and in this way we substitute the perimeter of the polygon by the length of the circumference and its apothem by the radius. With this reasoning we arrive at the formula with which we can find the area of ​​any circle: π x R2
As we increase the number of sides of a regular polygon, we observe that the length of the apothem gets closer and closer to the radius of the circle. This is why we can easily find the area of ​​a circle starting from the formula for the area of ​​a regular polygon. What we must do is replace the perimeter of the polygon by the length of the circumference and also the apothem by the radius:
Regular polygon area: perimeter x apothem

2
Perimeter = length
Radius = apothem
Diameter = 2 R (2 spokes)
R x R = R2
π = Pi (approximately 3.14)
So the area of ​​the circle = Area = π x D x Radius, where π x D = perimeter

2
Area = π x 2R x R = π x R2
2
Example of calculating the area of ​​a circle
1) A circular square has a radius of 500 meters. Calculate the area of ​​it.
We know that the area of ​​a circle is π x R2, so the area of ​​the square will be
π x 5002 = 785,000 m2.

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