The polygon represents the geometrical figure constructed by short circuit of a broken line. Distinguish several types of a polygon which differ depending on quantity of tops. Calculation of the area is made for each type of a polygon in the certain ways.
Instruction
1. Multiply lengths of the parties if you need to calculate the area of a square or rectangle. If it is necessary to learn the area of a rectangular triangle, complete it to a rectangle, to calculate its area and to divide it into two.
2. Use the following method for calculation of the area of polygons if the figure has no internal corners more than 180 degrees (convex polygon), at the same time all its tops are in knots of a grid of coordinates, and the broken line itself does not cross. Describe a rectangle that its parties were parallel to lines of a grid (axes of coordinates) around such polygon. At the same time at least one of tops of a polygon has to be rectangle top.
3. Break space in a rectangle into simple figures (triangles and squares). Find the area of each of them and put all received areas. Subtract the calculated areas of internal figures from the area of a rectangle. So you will find the area of a polygon quickly enough.
4. Apply one of below the presented formulas if it is necessary to calculate the area of a regular polygon (its corners and the parties are equal among themselves): – multiply quantity of corners (parties) of a polygon of n on two radiuses of r of the circle entered in it and on a tangent (π/n); – multiply (n/2) on two radiuses R circumscribed circles and on a sine (2π/n); – multiply (n/4) on two radiuses of r of an inscribed circle and on a cotangent (π/n).
5. Use the following formulas when the parties of a triangle are known: – multiply the parties of a triangle which prilezhat to a corner With, on a sine of this corner; – subtract from a poluperimetr (p) of a triangle at first one party (p-a), then other (p-b) and a third (p-c). Multiply the received values with poluperimetry and divide result into 2.
6. Apply to determination of the area of a trapeze formula S = h * (a + b) / 2 if height and both bases of a trapeze is known.
7. Use method of calculation of the area of a polygon by means of a palette. Draw around a polygon a square grid at which the party of one cage will be equal to unit that all tops of a polygon were in its knots.
8. Calculate the area of such figure on the Peak formula: S = In + G/2 – 1. Here In is a number of the knots of a grid located in a polygon, and – number of the knots of a square grid located on polygon border.