Area of the polygon

Geometry can rightfully be called one of the most ancient sciences, originating at the time of Euclid.

But even more than 4000 years ago the Egyptians produced the simplest geometric measurements and used practically the same methods as the scientists today.

The inhabitants of ancient Babylon made measurements of the simplest geometric figures using square units.

The standard of measuring the area from a long time has become a square - and all thanks to the simplicity of its construction, equal to the angles and sides.

Although in the territory of ancient Kievan Rus this measure was not taken for a long time. It is interesting that Rusich used different measures of the area of the earth, which did not express the accuracy of the measurements and were absolutely arbitrary. For example, in the calculation of the tax for the measure of the square, a unit was taken, measured by labor opportunities, and was called a "labor measure". The hayfields were measured with hay stumps - this was a "fruitful" measure. Naturally, all these measures were subjective and arbitrary, moreover, in different principalities sometimes did not correspond to each other, which caused considerable inconvenience. Approximately at the end of the 14th century, the word "tithe" began to occur in ancient writings in Rus. Its name was due to the fact that it was the tenth part of the side of the square, equal to one verst.

All this was only a conditional measurement of rectangles and triangles. And only the ancient Greeks knew how to find the area of a regular polygon. Although the term "area" they did not use, as well as did not use numbers in order to determine the area of the polygon.

In "Elements" Euclid studied the question of converting different figures into equal parts, taking a polygon as part of a plane bounded by a closed curve. Proceeding from the fact that the area of the figure does not change, if it is broken into its component parts and placed without intersection, he was able to establish that the area of the polygon can be calculated by adding the area of these figures.

The results of his works today find wide practical application, for example, among masters for laying tiles. For the area of the polygon they take the wall of a complex configuration. It is enough to calculate the number of tiles used for its cladding, and add up their area to find out the quadrature of this wall.

By quadrature is meant the area of the geometric figure. What is included in the definition of the area? To put it simply, this is a number that shows how many identical squares are included in the figure. Note that this is not a definition, but only a free interpretation. For the area unit of measurement, a square with a side equal to the unit of measurement of the segment is adopted. If a meter is used for this measurement, then the area, respectively, will be calculated in square meters, the square centimeter is determined in the same way, etc. The area of all geometric figures in the measurement is expressed by a number having a positive value.

In order to determine the area of a polygon, a certain formula is used, as well as dividing it into equal triangles. If the polygon has a complex shape, then you can try to break it into equal figures and by adding their areas to calculate the area of the original figure. Similarly, the area of a convex polygon is calculated.

A polygon can be convex if one of the following conditions is met:

- it lies on one side of the straight line, connecting its neighboring peaks;

- a polygon is the intersection of several planes.

Among other things, a convex polygon can be correct if all its sides and angles are equal. An example of this is a pentagon with equal sides.

The conclusion is one: the space around us, if you look closely, consists of various geometric figures, and knowledge of the laws of geometry and the ability to use them organically fit into our lives.