Parallelepiped – figures volume, characterized by existence of sides and edges. Each side side is formed by two parallel side edges and the parties of both bases corresponding each other. To find a side surface of a parallelepiped, it is necessary to put the areas of all of its vertical or inclined parallelograms.
Instruction
1. A parallelepiped – the spatial geometrical figure having three dimensions: length, height and width. In this regard it has two horizontal sides called the bases and also four side. All of them have the parallelogram form, but there are also special cases which simplify not only the graphic representation of a task, but also calculations.
2. The main numerical characteristics of a parallelepiped are the surface area and volume. Distinguish a full and side surface of a figure which turn out summation of the areas of the corresponding sides, in the first case – all six, in the second – only side.
3. To find a side surface of a parallelepiped, put the areas of four sides. Proceeding from property of a figure according to which opposite sides are parallel and equal write down: S = 2 · Sb1 + 2·Sb2.
4. Consider for a start the general case when a figure inclined: the bases lie in the parallel planes, but are displaced rather each other: Sb1 = · h; Sb2 = b · h, where and and b – the bases of each side parallelogram, h – parallelepiped.S height = (2•a + 2•b) • h.
5. Look attentively at the expression standing in brackets. Sizes an and b can be presented not only as the bases of side edges, but also as the parties of the basis of a parallelepiped, then this expression is nothing but its perimeter: S = P•h.
6. The inclined parallelepiped turns in a straight line if the angle between the basis and a side edge becomes right. Then height of a parallelepiped is equal to length of a side side: S = P • page.
7. A rectangular parallelepiped – a popular form of execution of many of a design: houses, pieces of furniture, boxes, models of household appliances and so forth. It is connected with simplicity of their construction / creation as all corners make 90 °. The side surface of such figure is similar to the same numerical characteristic direct, the difference between them is shown only when calculating a full surface.
8. A cube – a parallelepiped at which all measurements are equal: S = 4 · Sb = 4•a².