Planimetry is an important branch of geometry that studies flat shapes. The main property of all such elements is the area they occupy. Let's consider in the article, by what formulas, the calculation of the area of a circle is performed.
What it is?
Obviously, before calculating the area of a circle, a geometric definition of the figure should be given. It is understood as a set of points on a plane that are located from a specific point O at a distance less than or equal to R. Point O is called the center of the circle, and R is its radius.
Unlike a circle, a circle has a certain area. The circle limits the circle. Its length is the perimeter of the studied figure.
In addition to the radius and center, the circle is also characterized by a diameter D. It represents any segment that passes through the center of the figure.
A circle can be obtained if you take a certain segment, fix one of its ends on a plane, and rotate the free end around a fixed point 360 o . The length of the segment will be the radius of the figure.
Circle Area Formulas
The area of a figure is the area of a plane that is bounded by a circle. We will immediately find out that the area of the figure in question cannot be determined exactly, however, this accuracy can be increased to any significant digit after the decimal point. The thing is that in the area formula there is the number Pi (pi). Its approximate value was already known in ancient Egypt. However, accurate to a few decimal places, it was determined by Leonard Euler in 1737. He suggested calling it the "Pi number." It is up to five accuracy marks 3.14159.
The calculation of the area of the circle is carried out according to the following formulas:
S = pi * r 2 ;
S = pi * d 2/4;
S = L * r / 2.
The first two equalities are understandable, because they use the expression of the relationship between radius and diameter. As for the third formula, it turns out if we use the expression for the perimeter of the circle L. Recall that L = 2 * pi * r.
In the picture above you can see an example of solving the problem. The area in this case is indicated by the letter A.