Advice 1: How to find the cross section of the parallelepiped

Cross section of geometric figures of various shapes. The parallelepiped section is always a rectangle or square. It has a number of options that can be found analytically.
How to find the cross section of the parallelepiped
Using a box can hold four sections, which are squares or rectangles. He has two diagonal and two cross-sections. They usually have different sizes. The exception is the cube, which are the same.
Before you build section of the box, make a representation that represents this figure. There are two types of parallelepipeds - normal and rectangular. Conventional parallelepiped facets are at an angle to the base, they are rectangular and perpendicular to it. All faces of a rectangular parallelepiped are rectangles or squares. It follows from this that a cube is a special case of a rectangular parallelepiped.
Any section of a parallelepiped has certain characteristics. The main ones are area, perimeter, length of the diagonals. If the conditions of the problem known to the parties section, or any other parameters, this is enough to find its perimeter or area. The parties determined also diagonal sections. The first of these parameters - the area of the diagonal section.
To find the area of the diagonal section, you need to know the height and base side of the parallelepiped. If the length and width of the base of the box, then find the diagonal by using the Pythagorean theorem:
Finding the diagonal and knowing the height of a cuboid, calculate the cross-sectional area of a parallelepiped:
The perimeter of a diagonal cross-section is also possible to calculate two values - the diagonal of the base and the height of the parallelepiped. In this case, first find the two diagonals (upper and lower grounds) by the Pythagorean theorem, and then fold over with double height.
If we draw a plane parallel to the edges of the parallelepiped, it is possible to obtain the cross-section is rectangle, the sides of which are one side of the base of the box and height. The area of this section find the following:
The perimeter of this section find in the same way according to the following formula:
The latter case occurs when the section passes in parallel to the two bases of the parallelepiped. Then its area and perimeter equal to area value and the perimeter of the grounds, ie:
S=a*b - cross-sectional area;


Advice 2 : How to build a cross-section of a parallelepiped

In many textbooks there are jobs associated with the construction of sections of various geometric shapes including parallelepipeds. To cope with this task, you should be armed with some knowledge.
How to build a cross-section of a parallelepiped
You will need
  • paper;
  • - handle;
  • - the range.
On a sheet of paper, draw a box. If your task says that the box needs to be rectangular, make it square corners. Remember that opposite edges must be parallel to each other. Name its vertices, for example, S1, T1, T, R, P, R1, P1 (as shown in the figure).
How to build a cross-section of a parallelepiped
On the verge SS1TT1 put 2 points: A and C, let point a be on the segment S1T1 and a point on the segment S1S. If your task doesn't say where it should be these points, and do not specify the distance from the vertices, put them arbitrarily. Draw a straight line through points A and C. Continue this line to its intersection with the line segment ST. Label the point of intersection, let it be a point of M.
Put a point on the segment RT, label it as point B. draw a straight line through the points M and B. the intersection of this line with the edge of the label SP as point K.
Connect the points K and C. They must lie on the same face PP1SS1. Then through point B draw a straight line, parallel to the segment of the COP, will continue the line to the intersection with an edge of R1T1. The intersection of the label as point E.
Connect the points A and E. then select the resulting polygon ACKBE a different color – this will be a cross section of a given parallelepiped.
Remember that when you build a cross-section of the parallelepiped is possible to connect only those points that lie in the same plane, if you had enough points for the build section, add them by extending the line segments to the intersection with the face on which the desired point.
Useful advice
Only the parallelepiped can be constructed of 4 sections: 2 diagonal and 2 transverse. For clarity, select the resulting polygon cross section, this can just stroke or stroke it in a different color.
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