The quadrangle can be correct or have any form. For the correct figures ratios between elements are known. These communications are expressed by the formulas allowing to find the parties through other parameters.
Instruction
1. The parallelogram and a trapeze belong to the correct quadrangles. If all parties of a parallelogram are equal, such figure is called a rhombus. If at a parallelogram all four corners straight lines, then it is a rectangle. A special case of a rectangle — a square.
2. Let's say the set quadrangle — a square. If its perimeter is known, then the party is equal to the one fourth part of perimeter. For calculation of the party of a square on its area it is necessary to take a square root from the number equal to the area. If diagonal is known, for finding of the party divide diagonal into a square root from number two.
3. If it is necessary to define the parties of a rectangle or a parallelogram, the nobility only perimeter or the area is not enough. It is necessary to know in addition a ratio between the parties. Let's designate one party of a parallelogram (rectangle) of N, then other party of kN. If the value k is known, then the parties can be calculated through perimeter P on formula N = Р/2(1+k) or through the area of S on a formula N= √ (S/k).
4. In a parallelogram of the party it is possible to calculate if except the area and perimeter of a figure the corner ά between the parties is set. Finding of one of the parties of a parallelogram comes down to the solution of a quadratic equation of a look:²-NhP/2+S=0gde's N of N — the party of a parallelogram P — S parallelogram perimeter — the area of a parallelogram. Find the second party of the M parallelogram from S=NхMхSinά Square formula
5. It is also possible to find the parties of a trapeze on the known area and perimeter of a figure if the corner between the basis of a trapeze and its side is set.
6. For finding of the parties of any quadrangle divide a figure the auxiliary line into two triangles. Apply the known formulas of a ratio of elements of a triangle. For the possible solution of a task not only the area and perimeter of a figure, but also size of corners of a quadrangle have to be known.