Advice 1: How to find the area of irregular shapes

In the school course of geometry students mostly consider square and regular polygons. Meanwhile, to solve many practical problems often have to deal with irregular geometric figures. With this problem people faced when determining the size of suburban area or local area, and to calculate the amount of fabric for sewing, and in many cases. To calculate the area of irregular shapes in several ways.
How to find the area of irregular shapes
You will need
  • - irregular geometric figure;
  • measuring tools;
  • - transparent plastic;
  • - the range;
  • - gon;
  • - ballpoint pen.
Consider the geometric shape and determine what parameters of it are known to you. It can be the lengths of the sides or corners. Depending on the specified parameters and select the method of determining the area. For example, divide it into multiple shapes, the formulas for calculating the area of which you know. One of the most common methods is to swipe diagonally from one corner to all other vertices. In this case, you need to know the formula for calculating the area of an arbitrary triangle. But nobody forbids to divide a given shape and other polygons. For example, in the calculation of floor space in a room with a niche to separate the irregular figure into two rectangles or squares.
To determine the area is not too big of a part, use the palette. It is possible to do yourself. Cut a rectangular piece of any transparent plastic. Divide it into squares, the area of which you are aware — for example, 1x1 or 0,5x0,5 cm Ruler and a square to be exact. Apply the palette to the item. Count full squares, then incomplete. The number of incomplete squares, divide by 2 and add the result to the number of whole. The smaller the graduations on the palette, the more accurate the result. Similarly we can calculate square footage. The role of samples will carry out a grid of squares with sides 1x1 m drawn on the ground or marked with pegs between them with outstretched cords. We can restrict and marking of territory at the strip. .
With large squares alternatively. Take the most accurate site plan or local area. Define the scale. Use one of the following ways. Then the number of square inches put in the necessary scale.
Useful advice
In the manufacture of flat parts out of metal, you can calculate their size by using standard weighing. Cut out the actual part and the standard — a square, whose area is convenient to calculate. Do they need from the same material, and the thickness of the sheet should be the same and negligible. Calculate the mass ratio, and on it is an unknown area. However, this is not a very accurate method and apply it only in extreme cases.

Any irregular shape can be represented in a graph. Each point has its own coordinates. Imagine each segment as the graph of the function. Square footage from x-point to it is a definite integral. Calculate all the integrals. The area of the shape define by using the difference of integrals with a higher or lower value. This is a fairly time consuming method but it gives the greatest accuracy.

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.
In area to identify the parties
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.
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.
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.
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.
The calculation of the sides of other shapes having sides different in length to each other, requires knowledge of more variables.
Is the advice useful?