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How to Find the area of ​​the figure

How to find the area of ​​the figure

To be able to find the area of ​​the figure can be useful after graduation.

For example, this knowledge will come in handy if you are doing repairs, and want to know how much paint is required for the surface of an arbitrary shape.

Or suddenly you wanted to create a flower garden, and to calculate the amount of materials needed, determine its area.



It is convenient to operate, if your figure -polygon. You can always break it up into a finite number of triangles, and you alone is enough to remember the formula - the calculation of the area of ​​triangle. Thus, the area of ​​the triangle? It is half the product of the length of its side at the height of the length held to that same side. By adding up the individual areas of triangles, in which your will is transformed more complex form, you will find the desired result.


It is more difficult to solve the problem with the definition of the area of ​​an arbitrary shape. In such figure may be not only straight but also curved boundary. There are ways to approximate calculations. Simple.


First, you can use mosaic. This instrument made of transparent material deposited on its surface a grid of squares or triangles with a known area. Imposing pallets on top of the figure, which are looking for an area, you recalculate the number of your units that overlap the image. Combine fully closed unit with each other, complementing them in mind to complete. Next, multiply the area of ​​one mosaic figures on the number that is calculated, you will know the approximate area of ​​your arbitrary figure. It is clear that the more the grid is applied to your mosaic, the more accurate your results.


Second, you can in an arbitrary boundariesfigures to determine which area to outline the maximum number of triangles. Determine the area of ​​each square and fold them. This is a very approximate result. If you wish, you can also separately identify segments of the area bounded by arcs. To do this, imagine that the segment - a part of the circle. Draw the circle, and swipe to the radius of the arc after the edges of the center. The segments form an angle?. The area of ​​the sector is determined by the formula? * R ^ 2 *? / 360. Each smaller parts of your figure, you define the area and get the overall result, the obtained values ​​folded.


The third way is more difficult, but more specifically for someoneeasier. The area of ​​any shape can be determined using the integral calculus. The definite integral function shows the area of ​​the graph of the function up to the abscissa. The area enclosed between the two graphs, you can determine by subtracting the definite integral, with a smaller value of the integral in the same boundaries, but with great value. To use this method convenient to transfer your custom shape in the coordinate system and further define their functions and methods of work of higher mathematics, which here and now we will not go.

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