# Area of ​​the polygon

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geometry can rightly be called one of the most ancient sciences, originating in the times of Euclid.

But even more than 4000 years ago, the Egyptians made simple geometric measurements and used virtually the same methods that scientists today.

inhabitants of ancient Babylon, made measurements of simple geometric shapes using square units.

reference measurement area for a long time was the square - and all thanks to the simplicity of its construction, equal angles and sides.

Although the territory of the ancient Kievan Rus, this measure was not taken for a long time.An interesting fact is that the ancient Russians used a different measure of land area, which did not express the accuracy of measurement, and were completely arbitrary.For example, in calculating the taxes for the measure taking area unit, measured job opportunities, and he called it "a measure of labor."Grasslands measured haystacks - it was "fruitful" measure.Naturally, all these measures were subjective and arbitrary, in addition to various principalities sometimes do not match each other, causing significant inconvenience.Around the end of the 14th century in the ancient writings in Russia begins the word "tithe."It received its name due to the fact that is the tenth part of the square, equal to one less than a mile.

All this was only a nominal dimension 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 not to use the number to determine the area of ​​a polygon.

in the "Elements" of Euclid studied the question of transformation of various figures in the equal-taking of the polygon of the plane bounded by a closed curve.Based on the fact that the area shape does not change if its divided into parts and arranged without intersection, he was able to establish that the area of ​​the polygon can be calculated by summing the area of ​​these figures.

results of his works is today widely practical application, for example, among the masters of tiling.For the area of ​​the polygon they take the wall of complex configuration.Just count the number of tiles used for its lining and fold their area to find the quadrature of the wall.

By squaring means the area of ​​geometric shapes.What is included in the general definition of the area?To put it simply, it is a number that indicates how many equal squares included in the figure.Note that this is not a definition, but only a free interpretation.The unit of area measurement is taken square with a side equal to one measurement interval.If this measurement is used to meter the area, respectively, shall be calculated in square meters, and is defined similarly square centimeter, etc.The area of ​​all geometric shapes in the measurement expressed as the number of positive significance.

order to determine the area of ​​a polygon, using a specific formula, as well as its division into equal triangles.If a polygon has a complex shape, you can try to split it into equal pieces and by adding them to the area to calculate the area of ​​the originally specified shape.Similarly, the calculated area of ​​a convex polygon.

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

- it lies on one side of the line connecting it to neighboring vertices;

- polygon is the intersection of several planes.

In addition, a convex polygon can be right, if all the sides and angles are equal.An example of this is a pentagon with equal sides.

one conclusion: the space surrounding us, if you look closely, is composed of different geometric shapes, and knowledge of the laws of geometry and the ability to use them to fit perfectly into our lives.