There are an infinite number of plane figures of various shapes as right and wrong.The common property of all the pieces - each of them has an area.Square shapes - is the size of the plane occupied by these figures, expressed in specific units.This value is expressed is always a positive number.The unit area is a square whose side length is equal to one (e.g., one meter or one centimeter).Approximate area of any shape can be calculated by multiplying the number of unit squares into which it is divided on the area of one square.
Other definitions of this concept are as follows:
1. Areas of simple shapes - scalar positive values that satisfy the conditions:
- have equal pieces - equal to the value of the area;
- if the figure is divided into parts (simple shapes), its area - the amount of space these figures;
- square having side unit of measurement is the unit area.
2. Square shapes of complex shape (polygon) - positive value of having properties:
- have equal polygons - the same values of the area;
- if the polygon is a few other polygons, an area equal to the sum of the areas of the latter.This rule holds true for non-overlapping polygons.
accepted as an axiom the statement that the square shapes (polygons) - positive values.
Definition area of a circle is given separately the quantities sought by the area of a regular polygon inscribed in a circle of circles - despite the fact that the number of parties tends to infinity.
irregularly shaped area of the figure (arbitrary figures) do not have a definition, defined only by means of their calculations.
calculate the area in ancient times was an important practical problem in determining the size of land.Rules for calculating the area of a few hundred years BC the Greek scientists have been formulated and presented in the "Elements" of Euclid as theorems.Interestingly, the simple rules for determining areas in which figures - the same as in the moment.Square geometric shapes with curved contour, is calculated using the limit.
calculate the area of simple shapes (triangle, rectangle, square), all friends from school, is quite simple.Optionally, even remembering letter symbols containing the formula area figures.It is enough to remember a few simple rules:
1. To calculate the area of a square, you need to multiply the length of his hand on itself (or to build in the second degree).
2. The area of the rectangle is calculated by multiplying the length by the width.It is necessary that the length and width are expressed in the same units.
3. The area of the complex figure is calculated by dividing it into several simple and complicated area received.
4. diagonal rectangle divides it into two triangles whose areas are equal and are equal to half of its area.
5. The area of the triangle is calculated as the product of half of its height and base.
6. The area of the circle is equal to the product of the square of the radius throughout a certain number of «π».
7. The area of a parallelogram is calculated as the product of adjacent sides and the sine of the angle lying between them.
8. The area of the rhombus - ½ multiplication result of internal diagonals of the sine of the angle.
9. The area of a trapezoid is found by multiplying its height by the length of the median line, which is equal to the average of the bases.Another option of determining the area of the trapezoid - multiply its diagonal and the sine of the angle lying between them.
children in elementary school, for clarity, are often given the task: to find the area of the figure drawn on paper with the help of mosaic or a transparent sheet of paper bordered on the cells.This paper is superimposed on the measured figure is considered to be the number of complete cells (unit of area), place it in the loop, then the number of single-parent, which is divided in half.
