One of the figures considered at lessons of mathematics and geometry is the triangle. A triangle - a polygon which has 3 tops (corner) and 3 parties; the part of the plane limited to three points, in pairs connected by three pieces. There is a set of the tasks connected with finding of various sizes of this figure. One of them – the area. Depending on basic data of a task there are several formulas for determination of the area of a triangle.
Instruction
1. If are known to you length of the party and and the triangle h height which is carried out on it, use formula S =? h*a.
2. The area can be found in a rectangular triangle in such ways: a) if length of legs is known and and b, a formula looks so S = a*b/2; b) if there are a circle entered in a rectangular rectangle and a circumscribed circle and also their radiuses are known, then use formula S=r2 + 2rR.
3. The task is solved on determination of the area of a triangle in which lengths of all parties of a versatile triangle are specified through poluperimetr. At first find out triangle perimeter on a formula p=? (a+b+c). Further use a formula S=vp * (p-a) * (p-b) * (p-c).
4. In a task only length of one party of a triangle can be specified, but on type it is equilateral, then you will need formula S=a2 v3/4.
5. In statements of the problem sizes of corners and also lengths of the parties, adjacent to them, are known. For the solution of such tasks there are formulas: a) S=? a*b*sin? - if the corner and lengths of two parties, adjacent to it are known; b) S=c2/2 * (ctg? + ctg?) – here it is necessary to know length of the party and size of two corners adjacent to this party; c) S=c2 * sin? * sin? / 2 sin * (? +?) – if length of the party and corners, adjacent to it, are known. d) If only corners and one of the parties are specified, then find the area on the following formula S= a2 * sin? * sin? / 2 sin?, where and – the party, opposite to a corner?.
6. For a task where there are lengths of all parties and radius of a circumscribed circle, choose such formula S = by a*b*c/4R.
7. In a task of finding of the area all corners and also radius of a circumscribed circle are known to you. For this option of tasks use formula S=2R2 * sin? * sin? * sin?.
8. Besides the described and inscribed in a circle triangles, there are circles concerning one of the parties. The area is in such tasks of a formula S= (p-b) * rb where r – poluperimetr a triangle, b – the party of a triangle, rb - the radius of the circle concerning the party of b.