Sections of geometrical figures have various forms. At a parallelepiped the section always represents a rectangle or a square. It has a number of parameters which can be found in the analytical way.
Instruction
1. Through a parallelepiped it is possible to carry out four sections which represent squares or rectangles. In total it has two diagonal and two cross sections. As a rule, they have the different sizes. An exception is the cube at which they are identical. Before building parallelepiped section, make idea of what is represented by this figure. There are two types of parallelepipeds - usual and rectangular. At a usual parallelepiped of a side are located under some corner to the basis, and at rectangular they are perpendicular to it. All sides of a rectangular parallelepiped represent rectangles or squares. It follows from this that the cube is a special case of a rectangular parallelepiped.
2. Any section of a parallelepiped has certain characteristics. The main of them are the area, perimeter, lengths of diagonals. If from a statement of the problem the parties of section or any other its parameters are known, it is enough to find its perimeter or the area. Also diagonals of sections are determined by the parties. The first of these parameters - the area of diagonal section. To find the area of diagonal section, it is necessary to know height and the parties of the basis of a parallelepiped. If length and width of the basis of a parallelepiped are given, then find diagonal on Pythagorean theorem: d= √ a^2+b^2. Having found diagonal and knowing parallelepiped height, calculate parallelepiped cross-sectional area: S=d*h.
3. The perimeter of diagonal section can be calculated in two sizes too - the diagonal of the basis and height of a parallelepiped. In this case in the beginning find two diagonals (top and lower bases) on Pythagorean theorem, and then put with the doubled value of height.
4. If to carry out the plane parallel to parallelepiped edges, it is possible to receive the section rectangle which parties are one of the parties of the basis of a parallelepiped and height. Find the area of this section as follows: S=a*h. Find perimeter of this section the same way on the following formula: p=2 * (a+h).
5. The last case arises when section passes parallel to two bases of a parallelepiped. Then its area and perimeter are equal to value of the area and perimeter of the bases, i.e. :S=a*b is cross-sectional area; p=2 * (a+b).