It is easy to calculate square meter. The necessary mathematical formula for rectangles is studied in the second class. Difficulties can arise with calculation of the area of non-standard figures. For example, if it is about a pentagon or more difficult configuration.
It is required to you
- measurements of the parties and corners of a figure, paper, pencil, ruler, protractor.
Instruction
1. Represent the necessary figure on paper. Or draw the plan of the territory which area you are going to count. It will help for further calculations.
2. Break an initial figure into simple details: rectangles, triangles or sectors of a circle. Calculate the area of the received parts. For rectangles multiply lengths of the parties: S = a·b.
3. Determine the area of a triangle in any convenient way. Generally it can be calculated on several formulas. If there is a triangle with corners α, β, γ and opposite to them the parties of a, b, c, then its area is defined by S so: S = a · b · sin (γ)/2 = a · with · sin (β)/2 = b · with · sin (α)/2. In other words, choose a corner which sine will be to calculate the easiest, increase by the work of two next parties and divide in two.
4. Use other method: S = a²\· sin(β) · sin(γ) / (2·sin (β + γ). Besides, there is Heron's formula: S = √ (p · (p – a) · (p – b) · (p – c)) in which r is poluperimetr a triangle (p = (a + b + c)/2), and √ (...) — designation of a square root. There are also other ways. If you have a rectangular or equilateral triangle, then calculations become simpler. In the first case use length of two legs adjacent to a corner 90 °: S = a · b/2. Measure in the second at first height of an isosceles triangle lowered on its basis. Also use formula S = h · with / 2 where h is height, and with - basis length.
5. Calculate the area of the sector of the circle included in a required figure. For this purpose find the work of a half of length of an arch of the sector on circle radius. The most difficult in this task is an obtaining the correct value of radius for the sector allocated from an initial figure.
6. Put the received areas for final result.
7. Use a triangulation method for calculation of the area of difficult figures like pentagons. Break your source code into triangles. Calculate their areas and put results.