The quadrangle has four parties which can be found through such parameters as a corner, the area, diagonal. Tasks on finding of the area of a quadrangle very often meet it is aware of geometry.
Instruction
1. The simplest option of a quadrangle is called a rectangle. It has four parties, at the same time the parallel parties are among themselves equal. The parties perpendicular each other form among themselves the corner equal to 90 degrees. One of these parties is called length, and another, perpendicular to it - width. Multiplication of length by width it is possible to calculate the area of a rectangle. From this it is possible to draw a conclusion that the party of a rectangle, for example, width of a can be found, having divided the square at length: a=S/b. If in a task the square is given, then the party can be found on a formula: a= √ S as the parties of a square are equal.
2. To find the area of a parallelogram slightly more difficult, than the similar parameter of a rectangle. For an example draw a parallelogram with the parties of an and b and a corner α. If height and the area of a parallelogram are given, find the party on the following formula: a=S/h where h is height of a parallelogram, S - the area of a parallelogrammayesla in a task are given the party and a corner α and also the area of a parallelogram, a formula will change as follows: a=S/b*sinαРомб represents an equilateral parallelogram therefore the formula of finding of the area of a rhombus registers in the following look: S=a^2*sinαОтсюда, the party of a rhombus is equal: a= √ S/sinα
3. One more kind of a quadrangle - a trapeze. It has also four parties, but they not always are equal. At a trapeze the first two parties are the bases, and remained - sides. Draw an isosceles trapeze with two parties - the bases and a corner α at the basis. From the drawing it is visible that when carrying out a perpendicular to the basis the rectangular triangle is formed. If to carry out two projections, then two rectangular triangles which are equal will turn out. Find a smaller leg of a triangle by subtraction of lengths of the bases. After that, knowing a corner, find trapeze side.