First of all, we define what a polyhedron is. This is a three-dimensional geometric figure, the edges of which are presented in the form of flat polygons. The uniform formula for searching the volume of the polyhedron does not exist, since polyhedra are of different shapes. In order to find the volume of the complex polyhedron, it is conditionally divided into several simple, such as parallelelepiped, prism, pyramid, and then fold the volumes of simple polyhedra and are obtained as a result of the desired volume of the shape.
How to find a polyhedron - parallelepiped
To begin with, we find the area of \u200b\u200bthe rectangular parallelepiped. In such a geometric shape, all the faces are presented in the form of flat rectangular figures.
- The simplest rectangular parallelepiped is a cube. All cube ribs are equal to each other. In total, such a parallelepiped 6 faces, that is, 6 identical squares. The volume of such a figure is calculated in this way:
where a is the length of any edge Cuba.
- The volume of rectangular parallelepiped, the sides of which have different measurements, is calculated by the following formula:
where A, B and C - the length of the ribs.
How to find a polyhedron - inclined parallelepiped
The inclined parallelepipeda also also 6 faces, 2 of them - the foundations of the figure, 4 more - side faces. The inclined parallelepiped differs from the direct fact that its side faces relative to the base are not at a right angle. The volume of such a figure is calculated as a product between base area and height:
where S is the area of \u200b\u200bthe quadrangle lying at the base, H is the height of the desirable figure.
How to find a polyhedron - prism
A volumetric geometric figure, the base of which is represented by a polygon of any form, and side faces - parallelograms that have shared sides with the base - called prism. The prism has two bases, and the side faces as much as the sides of the figure, which is the basis.
To find the volume of any prism, both direct and inclined, multiplies the base area to height:
where S is the area of \u200b\u200bthe polygon at the base of the figure, and H is the height of the prism.
How to find a polyhedron - Pyramids
If a polygon is located at the base of the figure, and the side faces are presented in the form of triangles, closed in a total vertex, then such a figure is called a pyramid. It differs from the above figures in that it has only one base, in addition, it has a vertex. To find the volume of the pyramid, its base is multiplied by height, and share the result by 3:
Here s is the base area of \u200b\u200bthe desired geometric shape, and H is height.
The space of a simple polyhedron is quite simple, it is much more difficult to find the area of \u200b\u200bthe figure consisting of a plurality of polyhedra. Special attention will be paid to the proper separation of a complex polyhedron to simple.
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