Both at mathematics lessons, and in various practical affairs it is regularly necessary to face need to find the area of any given surface. It is necessary when calculating amount of materials on construction, when planning the land plots, at production of details on the machine. Ability to solve school geometrical problems in this case are very useful.
It is required to you
- - a solid with the set parameters;
- - measuring devices;
- - formulas of calculation of the area of geometrical figures.
Instruction
1. If it is necessary to calculate the surface area of half of the rectangular room or rectangular land plot, measure their length and width. Multiply results. In this case surface area is calculated on a formula S=ab where S is surface area, and and b — the parties of a rectangle. The formula of the area of a square will look as S=a2.
2. If the flat surface has more irregular shape, it needs to be divided into simpler parts which formulas of calculation of the area are known to you. For example, the wrong polygon can be divided into triangles or several triangles and a rectangle. At the same time consider the polygon parameters set in statements of the problem.
3. If you deal not with plane figures, and with solids, it is necessary to work likewise. In statements of the problem parameters of a figure which should be constructed or calculated are usually set. Attentively read conditions what area you should find. Almost each solid has a full surface area, the area of a side surface and the area of one or two bases.
4. Calculate the area of the bases. At a cone and a pyramid the basis one. The basis of a pyramid represents a polygon and is calculated on the corresponding formula. bases of correctquadrangularCalculate Square of a pyramid on a formula of the area of a square, that is having squared length of one of its parties. If in the basis of a pyramid the difficult polygon lies, divide it into simpler with parameters known to you. In the basis of a cone the circle, and respectively lies, the area is calculated by formula S=πR2.
5. Find the area of a side surface. At a rectangular parallelepiped it is calculated on a formula S=p*h where p – basis rectangle perimeter, and h – height. The surface area of a cube is calculated on formula S=4a2 as the side surface consists of 4 squares.
6. For calculation of a side surface of a cone it is the most convenient to make development. Find circle length on the set radius. It will be equal to length of an arch of a side surface of a cone. On length of an arch calculate the central corner, and then radius of a circle which sector is the side surface of a cone. Knowing these sizes, find the area of the sector, that is the area of a side surface of a cone.
7. For definition of a full surface of any given solid put among themselves the areas of a side surface and the bases.