Instruction

1

It is convenient to work if your figure is a polygon. You can always break it down into a finite number of triangles, and you have to remember only one formula for calculating the area of a triangle. So, the area of a triangle is half of the writing length to the length of the altitude drawn to this side. By adding up the areas of separate triangles, which are converted your will more complex form, you'll learn the desired result.

2

Harder to solve the puzzle and determined the area of an arbitrary shape. Such shapes can be not only straight, but curved boundaries. There are ways to approximate calculations. Simple.

3

First, you can use the palette. It is a tool of transparent material coated on its surface with a grid of squares or triangles with a known area. Putting the palette on top of the figures for which are looking for a square, you count the number of your units that overlap the image. Combine incompletely closed units with each other, complementing them in mind to complete. Further, by multiplying the area of one shape in the palette to the number that is calculated, you will know the approximate area your custom shapes. It is clear that the more frequent grid marked on your palette, the more accurate your result.

4

Secondly, you can within the boundaries of arbitrary shapes, which define the area, outline the maximum number of triangles. To determine the area of each and fold them square. This is a very approximate result. If you wish, you can also separately determine the area of the segment bounded by arcs. To do this, imagine that the segment is part of the circle. Construct this circle, and then from the centre spend the radii to the edges of the arc. The segments form an angle α. The whole area of the sector determined by the formula π*R^2*α/360. For each smaller part of your figure do you determine the area and get the overall result, adding the obtained values.

5

The third method is more complicated, but more accurate, and for someone easier. The area of any shapes can be determined using integral calculus. Definite integral of a function shows the area of the graph of the function to the abscissa. The area enclosed between two graphs, we can define subtraction of the definite integral, with a smaller value of integral in the same borders, but with great value. To use this method to conveniently transfer your arbitrary figure in a coordinate system and further define their functions and act in ways of higher mathematics, which here and now to delve will not.

Note

Gotta get to split uneven shape on the standard shapes (triangles, squares, rectangles, etc.), to calculate the area of each figure, and then folded. The total sum of squares is the area of the irregular figure. Find the area of the figure bounded by the lines

Useful advice

The area of plane figure — additive numerical characteristic shapes wholly owned by the same plane. In the simplest case, when a figure can be divided into finite set of unit squares, the area is equal to the number of squares. The formal introduction of the concept of area and volume can be found in the article as Jordan, here we give only the outline of the review. The area is a float function defined on a certain class of shapes in the Euclidean plane and satisfying...

# Advice 2: In area to identify the parties

Every year the task of geometry become more difficult. Is not enough to know how to count on ready-made formulas. You must be able to from a ready to bring a new formula to find out one way or the other.

Instruction

1

The calculation of the sides of the square. Formula of area of square A2 where a – side of this shape. To calculate the area of a square you need to know only one side, since all its sides are equal. Hence to calculate the direction is very simple: √. Example: the Area is 49. Select the square root of 49. Answer: 7.

2

The calculation of the sides of the rectangle. To find side of this figure, knowing only the value of square, impossible. There is one further value is its perimeter. Here is an example of an area of 12 and a perimeter 14.

Mark the sides of the rectangle "x" and "y". From the calculation formula of the perimeter P=2(a+b) substitute the values for our problem 2(x+y)=14.

The formula for calculating the area S=ab substitute the values for our problem XY=12, i.e. x=12. Substitute the value of "x" in the equation 2(x+y)=14.

Get 2(12/y+y)=14. Move like 12/y+y=14/2. 12/y+y=7. Multiply both sides of equation with "u". Get 12+y^2=7U. u^2-7U+12=0 is a quadratic equation, consider using the discriminant. The equation has 2 roots y=4; y=3.

Answer: the sides of the rectangle equal to 3 and 4 cm, respectively.

Mark the sides of the rectangle "x" and "y". From the calculation formula of the perimeter P=2(a+b) substitute the values for our problem 2(x+y)=14.

The formula for calculating the area S=ab substitute the values for our problem XY=12, i.e. x=12. Substitute the value of "x" in the equation 2(x+y)=14.

Get 2(12/y+y)=14. Move like 12/y+y=14/2. 12/y+y=7. Multiply both sides of equation with "u". Get 12+y^2=7U. u^2-7U+12=0 is a quadratic equation, consider using the discriminant. The equation has 2 roots y=4; y=3.

Answer: the sides of the rectangle equal to 3 and 4 cm, respectively.

3

The calculation of the sides of a rhombus. In order to know the sides of the diamond (EWYP), in addition to area have to have some value. For example, a height WH, it is the length of the perpendicular from vertex (W) on the side (EP). It should be remembered that the sides of a rhombus are equal. In this case, it is very easy to determine the side of the rhombus (EW). As you know, the rhombus can be thought of as two triangles EWP and PWY, each with an area equal to half the height works on the basis. It can be concluded that the area of the rhombus is equal to the product of the height to the length of a side. Hence, it turns out a simple formula to calculate the length of side diamonds: have its area divided by the length of the height - |EW|=S/|WH|. Example: Let the area of the rhombus EWYP equal to 20. And the height WH=5. Substitute the values in given formula: a |EW|=20/|5 . Answer: side equal to 4.

4

The calculation of the sides of an equilateral triangle. In order to know his side (and all sides are equal), in addition to area you must know the height. If you know these two values, then the calculation can be made for this formula: b=2S/h, where b is side of the triangle, S – area, h is the height. Example: Let the area of an equilateral triangle ABC is equal to 25. Height BH = 5.

Substitute values into the formula: b=2*25/5. Answer: the side equal 10.

Substitute values into the formula: b=2*25/5. Answer: the side equal 10.

Note

The calculation of the sides of other shapes having sides different in length to each other, requires knowledge of more variables.