Of the many geometric shapes of one of the most simple can be called a box.It has the shape of a prism whose base is a parallelogram.It is not difficult to calculate the area of the box, because the formula is very simple.
Prism make faces, vertices and edges.The distribution of these constituent elements performed in the minimum amount necessary for the formation of the geometric shape.A box contains 6 faces, which are connected by 8 vertices and 12 edges.And the opposite sides of the box will always be equal.Therefore, to identify the area of the parallelepiped is sufficient to determine the three dimensions of its faces.
parallelepiped (translated from the Greek term meaning "parallel faces") has some properties that are worth mentioning.Firstly, the symmetry of the shape is supported only in the middle of each of its diagonal.Secondly, having between any of the opposite diagonal vertices, one finds that all nodes have a common point of intersection.Also worth noting is the property that the opposite faces are always and necessarily be parallel to each other.
In nature, species are distinguished parallelepipeds:
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rectangular - consists of the faces of a rectangular shape;
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straight - has only lateral sides rectangular;
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oblique parallelepiped is a part of the side faces, which are set perpendicularity grounds;
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cube - consists of a square-shaped faces.
try to find the area of the box as an example of this type of rectangular shapes.As we already know, all its faces rectangular.And because the amount of these elements is reduced to six, then learned the area of each face, you need to sum up the result in a single number.And to find the area of each of them is not difficult.For this it is necessary to multiply the two sides of the rectangle.
used a mathematical formula to determine the area of a cuboid.It consists of the most significant characters representing face area, and is as follows: S 2 = (ab + bc + ac), where S - the area of the figure, a, b - side of the base, c - the lateral edge.
We give an approximate calculation.Assume, a = 20 cm, b = 16 cm, c = 10 cm. Now we need to multiply the number in accordance with the formula: 20 * 16 + 16 * 10 + 20 * 10 and obtain the number of 680 cm2.But it will be only half of the figure, as we have learned and summarize the three square faces.Since each face has its "double", to double the resulting value, and get the box area equal to 1360 cm2.
To calculate the lateral surface area, apply the formula S = 2c (a + b).The area of the base of the parallelepiped can be found by multiplying the length of the base at each other.
parallelepipeds in everyday life can be found frequently.About their existence reminds us of the shape of bricks, wooden drawer, normal matchbox.Examples of each can be found in abundance around us.School programs for the study of the geometry of the box set aside a few lessons.The first of these models show a rectangular parallelepiped.Then the students show how to enter in a ball or a pyramid, other figures, to find the area of the box.In short, it's just a three-dimensional figure.
