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.
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.