The need for finding of various elements including the areas of a triangle, appeared for many centuries BC at erudite astronomers of Ancient Greece. The area of a triangle can be calculated in various ways, using different formulas. The way of calculation depends on what elements of a triangle are known.
Instruction
1. If from terms tasks values of four elements of a triangle, such how corners are known to us??? and the parties of a, the area of a triangle of ABC is on a formula: S = (a^2sin? sin?) / (2sin?).
2. If from a condition values of two parties of b, c and a corner for them educated are known to us?, the area of a triangle of ABC is on a formula: S = (bcsin?)/2.
3. If from a condition values of two parties of a, b and the corner which is not formed by them are known to us?, the area of a triangle of ABC is as follows: We find a corner?, sin? = bsin? / a, further we determine a corner by the table. We find a corner?? = 180 °-?-?. We find the area of S = (absin?)/2.
4. If from a condition values only of three parties of a triangle of a, b and c are known to us, then the area of a triangle of ABC is on a formula: S = v (p(p-a) (p-b) (p-c)), where p – poluperimetr p = (a+b+c)/2
5. If from a statement of the problem height of a triangle of h and the party to which this height is lowered, then the area of a triangle of ABC are known to us is determined by a formula: S = ah(a)/2 = bh(b)/2 = ch(c)/2.
6. If values of the parties of a triangle of a, b, c and radius of R circle described about this triangle are known to us, then the area of this triangle of ABC is determined by a formula: S = three parties of a, b, c and radius of an inscribed in a triangle circle, the area of a triangle of ABC are known for ABC/4R.Esli is on a formula: S = pr, where p – poluperimetr, p = (a+b+c)/2.
7. If the triangle of ABC – equilateral, then the area is on a formula: S = (a^2v3)/4. If the triangle of ABC – isosceles, then the area is determined by a formula: S = (cv(4a^2-c^2))/4, where with – the triangle basis. If the triangle of ABC – rectangular, then the area is determined by a formula: S = ab/2, where an and b – triangle legs. If the triangle of ABC – rectangular isosceles, then the area is determined by a formula: S = c^2/4 = a^2/2, where with – a hypotenuse and the basis of a triangle, a=b – a leg.