Rectangle made of paper to print the diagram. Rectangular parallelepiped shape base. How to make a paper box. Unusual shape design option

22.09.2019

The rules of geometry, expressed in words and formulas, are often difficult to understand. If we translate them into the realm of the physical, make them visible, schoolchildren will quickly understand all kinds of theorems and axioms. Layouts of geometric shapes made from paper can help in this.

You will need

- paper;
- ruler;
- pencil;
- scissors;
- glue.

Instructions

1. In order to make a rectangular parallelepiped out of paper, you need to remember before everyone what he is. This shape has six faces, and each face is a rectangle. Consequently, the unfolded parallelepiped will consist of six rectangles lying in the same plane and joined together.

2. Decide on the desired size of the figure. Write down the values for 3 of its dimensions - length, width and height.

3. Select paper for bonding the visuals. A hefty thin one will not fit - it will warp too tightly from the glue and quickly fray. The cardboard may be too dense - it will not bend well or crack at the folds. Watercolor paper is optimal.

4. Draw a horizontal line on the paper. Its length is equal to the sum of the length and width, multiplied by two. From both ends of the line, perpendicularly downward, set aside segments equal to the height of the rectangular parallelepiped. Draw a line between these segments equal and parallel to the first horizontal line.

5. From the upper right corner of the resulting rectangle, set aside along the side face the number of centimeters equal to the width of the figure, and then a segment equal to the length of the parallelepiped. Later on, width and length again. Draw perpendicular lines from these points (down to the opposite side).

6. From the upper left corner of the universal rectangle, set aside the width of the rectangular parallelepiped, from the end of this segment perpendicular to the right - the length, and then perpendicular to the bottom - again the width. Draw the same shape on the opposite side of the rectangle, starting from its lower left vertex.

7. To make it easier to glue the figure, it is allowed to provide valves in the drawing. Draw a close rectangle 1.5 cm wide to the extreme side edge, cut its upper sides at an angle of 45 degrees. Attach three of the same valves to the parts, the construction of which was described in paragraph 6.

8. Cut out the workpiece and bend it along each drawn lines so that the side faces touch, and the upper and lower parts become the "bottom" and "cover" of the parallelepiped. Apply glue to the valves and tuck inward. Later, after the glue has dried, the visual model is allowed to be applied.

By showing your child different geometric shapes, you develop his spatial thinking. He begins to learn such representations as round, rectangular, square, spherical, cubic. Word " parallelepiped"The most difficult thing for a child. In order to master it, you can make this geometric figure together with it. By doing it with his own hands, he learns its validity.

You will need

- paper (rather thick, but not cardboard, so that it would be easier for the child to handle the craft), thick landscape paper is cooler;
- scissors;
- PVA glue;
- ruler;
- pencil.

Instructions

1. All parallelepiped but there are three components: length, width and height. First you need a sheet paper make the so-called "sweep". To do this, draw rectangles.

2. Draw the 1st rectangle (1) using the length and width representations. Possible, length 10 cm, width 3 cm. The result is a rectangle 10x3.

3. Next, you need to draw two rectangles 2 and 3 above and below, in which one side will be joint with rectangle 1 in length, and the width will be equal to the height. Perhaps it will be 5 cm. The result is rectangles 10x5.

4. Rectangle 4 has one side in length that is joint with rectangle 2, and the width is equal to the length of rectangle 1. The result is a 10x3 rectangle.

5. The last rectangles 5 and 6 are identical. They are located on either side of rectangle 1. Their width is equal to the width of rectangle 1, and their length is equal to the height parallelepiped a. So this is a 3x5 rectangle.

6. Draw 0.5 cm glue allowances on rectangles 3, 5 and 6. The flat pattern is ready. Significantly, in order for all the details to be severely measured and parallel, on the contrary, the figure will not exactly stick together and will have a sloppy appearance.

7. Cut out the flat pattern. Press the folds with the blunt end of the scissors, then bend. Glue the shape neatly using allowances. Spread them more abundantly so that the figure does not fall apart.

The sphere can be made of paper. Such a sphere is suitable for a Christmas tree toy. However, in order to make a real sphere, paper is not good. Let's try to make it out of ... threads.

You will need

Paper, thread, glue, ball.

Instructions

1. Option 1. You need to cut sixteen identical circles. After that, bend their parts as shown by the dotted line on the top of the drawing. Later, you need to glue the bent parts together. In any place where the triangles connect, it is necessary to tie a thread (if the sphere is planned to be hung somewhere). Such spheres are excellently used as genuine Christmas tree decorations, only if they are made of velvet paper. Pentagons can be used instead of circles. Such spheres look even more exciting, only small toys.

2. Option 2. In order to make such a sphere, even glue is not required. It is enough to cut three circles out of thick paper and mark them as shown on the bottom of the drawing. The 3rd circle is bent in half and inserted into the hole in the second circle. Later, you need to unfold the folded sheet and combine the 2nd and 3rd circles on it. After that, the sheet is bent in the middle, and the edges of the first circle are bent and the 2nd and 3rd circles are inserted into the center of the hole formed. Later, all the circles unfold.

3. Option 3. Of course, the above options, although they are primitive in manufacturing, are not spheres in the harsh sense of the word. If a real sphere is needed, then it is allowed to make it from threads. To make a "thread" sphere, you will need scissors, a round balloon, a spool of thread, PVA glue and plastic dishes. In a plastic container, glue and water are poured in a ratio of about three to one and thoroughly mixed ... After that, the balloon is inflated. The threads are unwound and placed in a bowl with diluted glue, where they are kept for five minutes. Later, after the threads are saturated with diluted glue, the ball is carefully wrapped around them. In this case, you need to ensure that the layer of threads is uniform and there are no gaps left. In a day, the sphere is ready. It is enough to remove the ball by piercing it with a needle in advance.

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Many objects around us have the shape of a parallelepiped. Consequently, the rule for constructing this geometric body may be required in the most unforeseen situations. Say, if you decide to make a box, a cage for an animal, an aquarium. Or maybe you want to do paper plastics?

You will need

Copper wire with a diameter of 2 mm.
Nippers
Pliers
soldering iron
solder
ruler
square

Instructions

1. Define the parameters of the box. You need to know its length, width and height. Mark out a piece of wire prepared for the ribs of the upcoming model. Measure and cut 4 pieces equal to the length of the parallelepiped, 4 pieces equal to its width and 4 pieces equal to the height.

2. Take a wire “length”, and from 2 sides at right angles solder pieces equal to the width. Solder the 2nd long piece to the received part. It should be perpendicular to "width" and parallel to "length". Correctly do the second base. parallelepiped .

3. Lay the base of the parallelepiped on the table and solder one of the segments equal to the height to it at a right angle. Do the same for each four corners.

4. Solder the top plane at right angles to the resulting edges of the side surface. It should sit firmly parallel to the bottom base.

5. If you need a demo model of a parallelepiped for a lesson, then at this point it can be considered complete. If you make, say, modules for a children's building corner, then you need to cover the resulting frame with leather or dense fabric.

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Note!
The choice of material depends on the purpose of the box. It is better than each wire to take from yellow copper, because it is more elastic. It is allowed to use steel wire, but not from stainless steel. Aluminum wire is not suitable. It's more cool to take a tailor's metal square. For a model of a non-rectangular parallelepiped, you need to make patterns for the sides and carefully measure all the corners. The parallelism of the grounds in this case will have to be controlled extremely severely. It is more comfortable for everyone to use a metal ruler for this purpose.

Helpful advice
For paper plastic, you only need to make a unfolded parallelelepiped. It consists of 3 types of rectangles with gluing allowances. According to the same thesis, a cage frame is made for an animal or aquarium.

In order to make a postcard or seal the torn cover of a textbook, you need a paper rectangle given sizes. Make this rectangle pretty easy by applying a square.

You will need

- paper
- square
- pencil
- scissors

Instructions

1. In order to do rectangle from paper, it must first be drawn. Draw a line segment ab equal to one side on the paper. rectangle a.

2. Attach a square to one side of segment ab so that the angle of the square coincides with the end of the segment, and, having noted the required length, draw the second side rectangle a located at right angles to side ab.

3. Attach the square to the other side of the segment ab so that the angle of the square coincides with the other end of the segment, and draw the third side rectangle a, located at right angles to side ab and equal to the 2nd drawn side. To check the correctness of construction rectangle and, again measure the second and third drawn sides - they must be identical in length.

4. Build the missing fourth side rectangle a, primitively combining the free ends of the last 2 constructed sides. Now built rectangle allowed to cut with scissors.

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Helpful advice
- when building a rectangle, hold the square firmly so that it does not slide off - when choosing a square, give predominance to a square made of wood, because it does not leave blots on paper

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A parallelepiped is a three-dimensional geometric figure, at the base of which is a polygon, and the faces are parallelograms. Many schoolchildren find it difficult to comprehend this concept, and even more so to solve problems for calculating the area and volume of a parallelepiped. In order to help the child in mastering the knowledge of geometry, make a model of the figure with him out of paper.

How to make a white paper parallelepiped

The volumetric model is assembled from a stencil, which is easy to make yourself. Prepare: a sheet of A4 paper, a pencil, a ruler, scissors, glue.

Lay the sheet in front of you with the wide side (lengthwise). Divide from 2 sides its side part, equal to 21 cm, in half and draw a line.
Let's say that the height of the edge of the parallelepiped is 10 cm. Measure from the middle from the two edges up and down by 5 cm and connect the marks with segments.
To form the sides of the figure, set aside on the first and last lines alternately - 8, 5, 8, 5 cm. Connect the lines along the points to each other - you get the edges of the parallelepiped.
On the second and third vertical lines, mark 5 cm from their beginning and end (up and down), since we have a width of one side of 5 cm and connect the ends of the segments, getting a quadrangle.
Step back from the contour of the figure by 1.5 cm on each side and draw a rough outline, which will indicate the places for fastening.

Important: do not go over the protruding side rectangles, so as not to accidentally cut them later.

Cut out the resulting shape, cut off the ends of the gluing strips with corners.
Bend the workpiece along the edges, washing them with your hands. Move the base to the other side so that the pencil grid stays inside, and push the basting all over the surface.
Glue the seam allowance on one side. Roll up the shape and, starting with the extreme strip, glue the opposite edge to it, then the upper base. Repeat the procedure on the other side and the box is ready.

How to make a rectangular parallelepiped out of paper - a cube

A cube is also a parallelepiped, only rectangular, the edges of which are squares. It is drawn in the same way as in the first version.

Construct sequentially four squares in the horizontal direction and two on the sides of the second along the vertical axis. Draw the flaps onto the glue.

Cut out the reamer, rinse the edges, glue the allowances and glue the cube.

How to make a paper box using origami technique

This method is good because you only need a square sheet of paper to make a figure.

Bend the sheet in half on both sides, divide the resulting corners in half so that the blank comes out of the folded triangles.

Flip the figure 90º. Fold the corners on the left and right until they touch, pressing the folds with your fingers. Put the sheet back side, repeat the steps.

Unscrew the folded corners and fold the others formed from the loose ends of the sheet and pointing with the vertices towards the folds.

Insert the corners into the resulting pockets.

Insert a pencil or blow into the hole formed at the bottom of the model, and the figure will acquire volume.

A paper box can be used not only as a visual aid to geometry. If the figures are made of colored cardboard, they will be useful in children's games, and made of decorative paper - they will help to beautifully pack a gift or souvenir.

By playing with your child with various geometric shapes, you help him develop spatial thinking and imagination. He begins to understand what it means to be square, round, cubic, spherical, rectangular, and he can easily imagine it in his head. Even students at school at a geometry lesson, teachers always show models of various figures, which contributes to a better assimilation of geometric theorems and axioms. And, perhaps, the most difficult and difficult to pronounce word for a child is "parallelepiped". In order to master this figure and understand its patterns, we suggest that you and your child make a paper box with your own hands.

To do this, you will need:

thick paper (but not cardboard, otherwise such a craft will bring a lot of difficulties to the child), you can use a sheet from the album;
pencil;
ruler;
scissors;
PVA glue.

To understand how to make a paper box, you need to remember how it looks and what it is. This shape has 6 faces, each of which is a rectangle. Consequently, the unfolding will consist of 6 interconnected rectangles located in the same plane.

1. Like any three-dimensional figure, a parallelepiped has length, width and height. It is on their value that the size of the resulting fake will depend. Let's define the desired values and write them down.

2. Let's start drawing a diagram of a rectangular parallelepiped on paper. Remember that the paper should not be too thin, it will easily get wet from the glue and warp, then the figure will not work out even, and an unnecessarily thick cardboard will not bend well and crack at the bends.

3. Draw a horizontal line, the length of which will be equal to the sum of the width and height, multiplied by two. Then, from each end of the line, we drop a perpendicular equal to the length of the assumed parallelogram. Draw a line between them parallel to the first.

4. Now, from the upper right corner, set aside the height of the parallelogram, after - the width. Then again the height, and again the width. From the points obtained, draw perpendicular lines to the opposite side, which will be equal to the length of the parallelogram. Thus, we got 4 faces of the shape. There are still 2 left.

5. Above the second rectangle on the right, add two more children from the bottom and from the top. In this case, from the second mark to the right, which we made in point 4, draw a perpendicular upward equal to the height of the figure. We repeat the same from the second mark. Let's connect the perpendiculars with a segment equal to the width of the parallelogram. Draw the bottom rectangle on the opposite side using the same method.

6. To make it easier to glue the paper parallelepiped, add additional "wings" to the drawing, as shown in the figure. Their width should be about 1.5 cm. You also need to make them beveled corners (45 degrees) so that when gluing they do not look out.

So, the unfolded paper parallelepiped is ready. It is important that all the details of the drawing are even and strictly measured, otherwise the figure will not stick together evenly and will be curved.

7. Cut out the workpiece and bend it along all the lines so that our side faces touch, and the upper and lower rectangles become the "bottom" and "cover" of the figure.

8. Lubricate the additional "wings" with glue and assemble the parallelepiped, tucking them inward. Let's wait for the glue to dry.

If you have mastered the manufacture of this figure, you can start collecting an oblique paper box, the edges of which are acute-angled rhombuses.

There may be many reasons when you need to make a parallelepiped yourself: school homework for completing a model of a simple geometric body, a desire to make or even a unique home interior design.

What does a three-dimensional polygon have to do with it?

To put it bluntly, all this is within the power of such a simple shape as a parallelepiped. It is the easiest and fastest way to make it out of paper. Consider the most interesting options: gluing a figure from a pattern according to a given drawing, origami and modular assembly.

Lesson # 1: 3D model

In order to make a rectangular parallelepiped out of paper, you will need cardboard, a ruler, a pencil and scissors.

First of all, you must know exactly what size the model you want to get. On a separate piece of paper, write down the main dimensions of the parallelepiped: the height of the side surfaces, length and width.

It is important not just to redraw the sample, but according to the required parameters. Then there will be no frustration and no need to do double work as a result.

When your diagram is ready, circle the resulting drawing with the edge of the scissors under the ruler. This must be done so that the cardboard folds neatly in places of fold, and does not "dictate" its lines.

In front of you is an unfolded parallelepiped. Cut the blank out of paper with your own hands. Fold it on the back along the marked lines.

It remains only to glue the side allowances from the inside to the adjacent sides of the model and your parallelepiped is ready.

Lesson # 2: Origami

As a child, you probably played with cubes. Of course, at the time you had no idea that you were dealing with parallelepipeds. In the course of the game, there is nothing to do with the parallelism of all sides, but functionality is important. And not to tell the child The main thing is that the delight of childhood can be repeated, but at a new level. How? Make a paper box using the origami technique. Yes, not one model, but as many as the bulbs on your halogen garland. See what you end up with.

Step 1

Take a square piece of paper. Fold it in half. Unfold and fold again on the other side.

Step 2

Repeat the same steps, only away from the corners.

Step 3

Keep two opposite sides of the sheet centered with your fingers. The other two opposite surfaces are also directed towards each other and smooth the resulting triangle, thereby fixing the new fold lines.

Step 4

First on one side, and then on the other, lift the corners of the triangle to the top.

Step 5

The result is the so-called rhombus. Bring its right and left corners together in the center. Smooth out the future paper box again.

Do not forget to turn over and bend the corners on the back.

Step 6

Do the opposite. Open the corners just bent and fold the others. They are formed from the free ends of the paper sheet and are directed by their vertices to the fold lines in opposite directions from each other.

All this is difficult to understand only until the moment you see what, in fact, is at stake.

Step 7

Insert the newly obtained corners into the resulting pockets, as shown in the example.

Step 8

So, the paper parallelepiped is ready! It's just still folded. There are two ways to add volume to it. First: inflate. Second: take a long rod from an ordinary ballpoint pen and use it. Both methods are carried out through the only hole that you find in the bottom of the model (the one closest to you). When you do these manipulations, you will get this wonderful shape:

Insert into the same hole through which the cube was inflated and

Lesson # 3: modular assembly

Another curious way to make a very nice paper box.

Step 1

Fold the square sheet in half and fold each half in half lengthwise. Let the two extreme folds "meet" in the center.

Learn how to make a rectangular box out of paper. A diagram and a detailed description will help you with this.

What materials will be needed

Thick sheets of A4 paper of white or other color;
- scissors;
- pencil;
- ruler;
- glue.

Before you start working on creating a shape, see or imagine how it will look. From the school course, you can recall that a parallelepiped has 6 faces and the same number of sides. Therefore, the diagram on paper will consist of six rectangles connected together in one plane.

Paper parallelepiped: step-by-step instructions

1. First you need to decide on the size of the figure, its length, width and height. Write down these values.

2. Now it is worth drawing a diagram on paper. Take the values of the height and width of the future box, add them and multiply them by two. Draw a horizontal line, its length should be equal to this value.

3. From the ends of the line, you need to lower two segments perpendicular to it, they must be equal to the length of the figure. Connect the segments together by drawing another line.

5. Look at the upper right corner of the resulting rectangle. From this point, you need to postpone two segments - height and width. After that - once again the height and width. Draw perpendicular lines from the marked points to the opposite side. You have 4 faces.

6. Pay attention to the second rectangle to the right, you need to draw two more below and above it. To do this, draw a line as long as the height of the figure. Then swipe another one and connect them. Repeat the same steps with the second rectangle from the bottom.

7. To make it easier to glue the whole shape, you need to add a few more small details, as shown in the picture. They should be about 1.5 cm wide and also beveled at 45 degrees.

8. The diagram of the figure is ready, carefully cut it out of paper, bend all the lines. The rectangles above and below will become the bottom and the roof of the box. In this case, all side faces must touch.

9. Apply glue to additional details, connect the shape. Let the glue dry. Your box is ready!

Now you know how to make a parallelepiped out of paper, photos and videos will help you correctly draw a diagram and assemble a shape.

A large selection of sweeps of simple geometric shapes.

The first acquaintance of children with paper modeling always starts with simple geometric shapes such as a cube and a pyramid. Not many people succeed in gluing a cube the first time, sometimes it takes several days to make a truly even and flawless cube. More complex shapes of a cylinder and a cone require several times more effort than a simple cube. If you do not know how to accurately glue geometric shapes, then it is too early for you to tackle complex models. Take care of yourself and teach your children to crate these "basics" of modeling using ready-made sweeps.

To begin with, I, of course, propose to learn how to glue a regular cube. The sweeps are made for two cubes, one large and one small. A small cube is a more complex shape because it is more difficult to glue it than a large one.

So, let's begin! Download a five-sheet sweep of all the shapes and print on thick paper. Before you print and glue geometric shapes, be sure to read the article on how to choose paper and how to properly cut, fold and glue paper in general.

For better printing, I advise you to use the AutoCAD program, and I give you sweeps for this program, and also read how to print from AutoCAD. Cut out the sweeps of the cubes from the first sheet, along the fold lines, be sure to draw a compass needle under the iron ruler so that the paper bends well. Now you can start glueing the cubes.

To save paper and for every fireman, I made several sweeps of a small cube, you never know you will want to glue more than one cube or something will not work out the first time. Another simple figure is a pyramid, you can find its sweep on the second sheet. The ancient Egyptians cost similar pyramids, though not made of paper and not so small :)

And this is also a pyramid, only unlike the previous one, it has not four, but three faces.

Sweep of a three-sided pyramid on the first sheet for printing.

And one more funny pyramid of five faces, its sweep on the 4th sheet in the form of an asterisk in two copies.

A more complex shape is a pentahedron, although a pentahedron is more difficult to draw than to glue.

Development of a pentahedron on the second sheet.

So we got to the complex shapes. Now you have to strain yourself, glueing such figures is not easy! To begin with, an ordinary cylinder, its sweep on the second sheet.

And this is a more complex figure in comparison with the cylinder, because at its base is not a circle, but an oval.

The sweep of this figure on the second sheet, two spare parts were made for the oval base.

To neatly assemble the cylinder, its parts need to be glued end-to-end. On one side, the bottom can be glued without any problems, just place the previously glued tube on the table, put a circle on the bottom and fill it with glue from the inside. Make sure that the diameter of the pipe and the round bottom fit tightly to each other, without gaps, otherwise the glue will leak and everything will stick to the table. The second circle will be more difficult to glue, so glue the auxiliary rectangles inside at a distance of paper thickness from the edge of the pipe. These rectangles will prevent the base from falling inward, now you can glue the circle on top without any problems.

A cylinder with an oval base can be glued in the same way as a regular cylinder, but it has a lower height, so it is easier to insert a paper accordion inside, and put the second base on top and glue it along the edge with glue.

Now a very complex shape - a cone. Its details are on the third sheet, a spare circle for the bottom on the 4th sheet. The whole difficulty of gluing the cone is at its sharp top, and then it will be very difficult to glue the bottom.

A complex and at the same time simple figure is a ball. The ball consists of 12 pentahedrons, a sweep of the ball on the 4th sheet. First, the two halves of the ball are glued, and then both are glued together.

Quite an interesting figure - a rhombus, its details on the third sheet.

And now two very similar, but completely different figures, their difference is only at the base.

When you glue these two figures together, you will not immediately understand what it is all about, they turned out to be completely imperceptible.

Another interesting figurine is a torus, but we have it very simplified, its details are on the 5th sheet.

And finally, the last figure of equilateral triangles, I don't even know what to call it, but the figure looks like a star. Sweep of this figure on the fifth sheet.

That's all for today! I wish you success in this difficult work!

To do this, you will need:

thick paper (but not cardboard, otherwise such a craft will bring a lot of difficulties to the child), you can use a sheet from the album;
pencil;
ruler;
scissors;
PVA glue.

7. Cut out the workpiece and bend it along all the lines so that our side faces touch, and the upper and lower rectangles become the "bottom" and "cover" of the figure.

8. Lubricate the additional "wings" with glue and assemble the parallelepiped, tucking them inward. Let's wait for the glue to dry.

If you have mastered the manufacture of this figure, you can start collecting an oblique paper box, the edges of which are acute-angled rhombuses.