The triangle is made by three parties which total length is called perimeter. The closed broken line formed by the parties of this figure is called perimeter too. It limits the site of a surface of a certain square. Lengths of the parties, perimeter, the area and also corners in tops - all this is connected among themselves by certain ratios. Use of these ratios will allow to calculate missing parameters of a figure, for example, its perimeter and the area.
Instruction
1. If lengths of each of the parties are specified in statements of the problem or you have an opportunity to independently measure them, it will be very simple to calculate perimeter length - put the sizes of three parties.
2. In the presence in initial conditions of information only on two parties (And yes C) and also about corner size between them (γ), begin calculation of perimeter (P) with finding of length of the missing party. Make it with application of the theorem of cosines. At first square lengths of the known parties and put results. Then take away from the received size the work of lengths of the same parties at each other and a cosine of the known corner. In a general view the formula of calculation of the unknown party can be written down so: √ (A²+B²-A*B*cos(γ)). To length of the third party received this way add lengths of two others, known from conditions, and calculate perimeter: Р = √ (A²+B²-A*B*cos(γ)) + And + Century.
3. Having learned in the course of calculation of perimeter or from statements of the problem of length of all parties of a figure (And, In and C), it is possible to start calculation of its (S) Square. These parameters - the area and lengths of the parties - are connected among themselves by Heron's formula. As on the previous step you already received a formula of calculation of perimeter, find its numerical value and use the received size for simplification of a formula. Divide perimeter in half and appropriate this value of an additional variable, having designated it by letter p. Then find differences between poluperimetry and length of each of the parties - all three values have to turn out. Multiply these sizes among themselves and increase on poluperimetr, and then take a square root from the calculated value: S= √ (p ∗ (p-A) ∗ (p-B) ∗ (p-C)).
4. It is possible to use simpler formula of calculation of the area (S) if to lengths of the parties received on the previous steps (And, In, C) to add the radius (R) of a circumscribed about a triangle circle. Make this formula of the work of lengths of all three parties, having added to it operation of division into quadruple radius. Such identity has to turn out at you: S=ABC / (4∗R).