Area or size of geometrical figures one of the most important sizes of geometry. For calculation and finding of the area of figures at the set parameters various formulas are formed. The problem of determination of the area in each case is solved taking into account properties of solids. For some figures, and in particular for a convex polygon, there are no accurately set formulas of calculation of the area. In this case the size of a figure decides on the help of additional constructions.
Instruction
1. For determination of the area of a convex polygon it is necessary to know its parties and corners. Write down the known data. Construct a convex polygon.
2. Carry out additional constructions. From one top of a polygon draw straight lines to other tops. Splitting a figure into several triangles will turn out. The area of a polygon consists of the sums of the areas of these triangles.
3. Determine the area of each triangle. The first calculate the area of a triangle of a, b, m with two known edges of an and b and a corner α between them. The area of a triangle calculates by formula S =? * a*b*sin α.
4. Further find an unknown third edge of m of this triangle and a corner, adjacent to this party, β. These data will be necessary for calculation of the area of the second triangle. The edge of m is according to formula m = and * sin α.
5. Determine an unknown corner β by a formula sin β = by m/and. Subtracting the received corner β from the polygon corner set originally γ, we find an unknown corner of the following constructed triangle. Now in the second triangle there are also two known edges of m, c and also corner between them equal γ - β. Find the same way its area, an unknown edge of n and the corner adjoining to it χ.
6. Calculate the areas of other triangles in the same way. Having received all values of the areas, put them. Total amount will also be equal to the area of a convex polygon.