Of the many geometric shapes, one of the simplest can be called a parallelepiped. It has the shape of a prism, at the base of which is located a parallelogram. It is not difficult to calculate the area of the box, because the formula is very simple.
The prism is made up of faces, peaks and edges. The distribution of these constituent elements is made in the minimum quantity necessary for the formation of this geometric shape. The box contains 6 faces, which are connected by 8 vertices and 12 edges. Moreover, the opposite sides of the box will always be equal to each other. Therefore, to find out the area of the parallelepiped, it is enough to determine the dimensions of its three faces.
The parallelepiped (translated from Greek as “parallel faces”) has some properties that should be mentioned. Firstly, the symmetry of the figure is confirmed only in the middle of each of its diagonals. Secondly, drawing a diagonal between any of the opposite vertices, you can find that all the vertices have a single intersection point. It is also worth noting the property that the opposite faces are always equal and will be necessarily parallel to each other.
In nature, there are such varieties of parallelepipeds:
rectangular - consists of faces of a rectangular shape;
straight - has only lateral faces rectangular;
the inclined box contains side faces that are not perpendicular to the bases;
cube - consists of square faces.
Let's try to find the area of the box using 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, having learned the area of each face, it is necessary to summarize the results in one number. And finding 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 box. 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, c is the side edge.
We give an approximate calculation. Suppose a = 20 cm, b = 16 cm, c = 10 cm. Now you 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 recognized and summed up the areas of three faces. Since each face has its own “double”, we need to double the resulting value, and we get the area of the box equal to 1360 cm2.
To calculate the lateral surface area, apply the formula S = 2c (a + b). The area of the base of the box can be found by multiplying the lengths of the sides of the base by each other.
In everyday life, parallelepipeds can be found often. The shape of a brick, a wooden desk drawer, an ordinary matchbox reminds us of their existence. Examples can be found in abundance around us. In school curricula in geometry, several lessons have been devoted to the study of the parallelepiped. The first of them demonstrate models of a rectangular parallelepiped. Then the students are shown how to fit a ball or a pyramid into it, other figures, find the area of the box. In a word, this is the simplest three-dimensional figure.