Be able to find the area of the figure can be useful after graduation.
For example, this knowledge is useful if you are doing repairs, and want to know how much paint is required for a surface of an arbitrary shape.
Or suddenly you want to create a flower garden, and to calculate the number of necessary materials, you should determine its area.
It is convenient to act if your figure -polygon. You can always break it into a finite number of triangles, and you only need to remember one formula - the calculation of the area of the triangle. So, the area of the triangle? It is half of the product of the length of its side by the length of the height drawn to this very side. Summing up the areas of individual triangles into which your will has transformed a more complex form, you will learn the desired result.
It is more difficult to solve the problem with the definition of the area of an arbitrary figure. Such a figure can have not only straight lines, but also curvilinear boundaries. There are ways for approximate calculation. Simple.
First, you can use a pallet. It is a tool made of transparent material with a grid of squares or triangles with a known area on its surface. By placing a pallet on top of the shape for which you are looking for an area, you recalculate the number of your units that overlap the image. Combine incompletely closed units of measurement with each other, complementing them in the mind to complete. Further, multiplying the area of one figure of the pallet by the number that was calculated, you will know the approximate area of your arbitrary figure. It is clear that the more frequent a grid is put on your pallet, the more accurate your result.
Secondly, you can within the boundaries of an arbitraryFigure, for which you define the area, outline the maximum number of triangles. Determine the area of each and add up their area. This will be a very approximate result. If you wish, you can also separately determine the area of segments bounded by arcs. To do this, imagine that the segment is part of the circle. Construct this circle, and afterwards from its center draw the radii to the edges of the arc. The segments form an angle between them. The area of the whole sector is determined by the formula? * R ^ 2 *? / 360. For each smaller part of your figure, you define the area and get the overall result by adding the values obtained.
The third method is more difficult, but more accurate also for someone,easier. The area of any figure can be determined using the integral calculus. The definite integral of the function shows the area from the function graph to the abscissa. The area enclosed between two graphs can be determined by subtracting a definite integral, with a smaller value, from the integral in the same boundaries, but with a larger value. To use this method, it is convenient to transfer your arbitrary figure to a coordinate system and then determine their functions and operate using higher mathematics methods, which we will not go into here and now.