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Calculate the area of the parallelepiped

Of the many geometric figures, one of the simplest is the parallelepiped. It has the form of a prism, at the base of which is a parallelogram. It is not difficult to calculate the area of a parallelepiped, since the formula is very simple.

The prism is made up of faces, peaks and edges. The distribution of these constituent elements is carried out in the minimum amount necessary for the formation of this geometric shape. The parallelepiped contains 6 faces, which are connected by means of 8 vertices and 12 edges. Moreover, the opposite sides of the parallelepiped will always be equal to each other. Therefore, in order to know the area of a parallelepiped, it is sufficient to determine the dimensions of its three faces.

A parallelepiped (translated from Greek as "parallel faces") has some properties that should be mentioned. First, the symmetry of the figure is confirmed only in the middle of each diagonal. Secondly, having spent between any of the opposite vertices a diagonal, you can find that all the vertices have a single point of intersection. Also worth noting is the property that the opposite faces are always equal and will be necessarily parallel to each other.

In nature, there are such types of parallelepipeds:

  • Rectangular - consists of faces of a rectangular shape;

  • Straight - has only lateral faces rectangular;

  • The inclined parallelepiped has lateral faces that are not perpendicular to the bases;

  • Cube - consists of faces of a square shape.

Let's try to find the area of a parallelepiped by the example of a rectangular type of this figure. As we already know, all its faces are rectangular. And since the number of these elements is reduced to six, then, knowing the area of each face, you need to summarize the resulting results into one number. And to find the area of each of them will not be difficult. To do this, multiply the two sides of the rectangle.

A mathematical formula is used to determine the area of a rectangular parallelepiped. It consists of symbolic symbols denoting faces, area, and looks like this: S = 2 (ab + bc + ac), where S is the area of the figure, a, b are the sides of the base, and c is the side edge.

We give an approximate calculation. Suppose a = 20 cm, b = 16 cm, c = 10 cm. Now we need to multiply the numbers in accordance with the requirements of the formula: 20 * 16 + 16 * 10 + 20 * 10 and get the number 680 cm2. But this will be only half the figure, since we learned and summed up the areas of the three faces. Since each face has its "double", it is necessary to double the resultant value, and we get the parallelepiped area equal to 1360 cm2.

To calculate the area of the lateral surface, use the formula S = 2c (a + b). The area of the base of the parallelepiped can be determined by multiplying the lengths of the sides of the base by one another.

In everyday life parallelepipeds can be found often. About their existence, we are reminded of the shape of a brick, a wooden box of a desk, a usual matchbox. Examples everyone can find in abundance around us. In the school programs on geometry, several lessons have been devoted to the study of the parallelepiped. The first of them demonstrate the models of a rectangular parallelepiped. Then the students are shown how to enter a ball or pyramid, other figures, to find the area of the parallelepiped. In a word, this is the simplest three-dimensional figure.

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