The pyramid is a reamer. Reaming of the pyramid for gluing. Paper sweeps

Rectangle, square, triangle, trapezoid andothers - geometric figures from the section of exact science. A pyramid is a polyhedron. The base of this figure is a polygon, and the lateral faces are triangles having a common vertex, or trapezium. For a complete presentation and study of any geometric object, mock-ups are made. Use the most diverse material from which the pyramid is made. The surface of a polyhedral figure unfolded on a plane is called its unfolding. Create a layout will help the method of converting planar objects into three-dimensional polyhedra and certain knowledge from geometry. The development of paper or paperboard is not easy to make. It will be necessary to be able to execute drawings according to the specified dimensions.

Materials and devices

Pyramid sweep

Modeling and execution of multifaceted volumetricgeometric shapes - an interesting and exciting process. From paper, you can perform a large number of all kinds of mock-ups. For work you will need:

  • paper or cardboard;
  • scissors;
  • pencil;
  • ruler;
  • compass;
  • eraser;
  • glue.

Defining parameters

First of all, we will determine what the pyramid will be. The unfolding of this figure is the basis for making a three-dimensional shape. The performance of the work will require extreme accuracy. If the drawing is incorrect, the geometric figure will not be collected. Suppose you need to make a layout of the right triangular pyramid.

Any geometric body has certainproperties. This figure has the base of a regular polygon, and its vertex is projected into its center. An equilateral triangle is chosen as the base. This condition defines the name. The lateral edges of the pyramid are triangles, the number of which depends on the polyhedron chosen for the base. In this case there will be three. It is also important to know the dimensions of all the components from which the pyramid will be composed. Paper sweeps are performed in accordance with all the data of the geometric figure. The parameters of the future model are discussed in advance. The choice of the material used depends on this data.

How is the correct pyramid scanned?

The basis of the model is a sheet of paper or cardboard. Work begins with a pyramid drawing. The figure is presented in expanded form. The flat image on the paper corresponds to the preselected dimensions and parameters. The right pyramid has a regular polygon base, and the height passes through its center. We make for the beginning a simple model. In this case it is a triangular pyramid. Determine the size of the selected shape.

Reaming the right pyramid
To build a sweep of the pyramid, the basewhich is the right triangle, in the center of the sheet, using a ruler and a pencil, draw the base of the given sizes. Further to each of its sides we draw the side faces of the pyramid - triangles. Now we turn to their construction. The dimensions of the sides of the triangles of the lateral surface are measured by a compass. We put the knife of the compass on the top of the painted base and make a notch. The action is repeated by moving to the next point of the triangle. The intersection resulting from such actions will determine the tops of the side faces of the pyramid. We connect them with the base. We get the drawing of the pyramid. For gluing a three-dimensional shape on the sides of the side faces, valves are provided. We finish the small trapezium.

Build the layout

Cut out the pattern with the scissors along the contour. Carefully bend the sweep across all lines. Trapezium valves are threaded inside the figure in such a way that its faces are closed. They are lubricated with glue. Thirty minutes later the glue will dry. The volumetric figure is ready.

Development of the quadrilateral pyramid

First, imagine how the geometricfigure, the layout of which we will make. The basis of the chosen pyramid is a quadrilateral. The lateral edges are triangles. For work we use the same materials and devices as in the previous version. The drawing is done on paper with a pencil. In the center of the sheet we draw a quadrilateral with the selected parameters.

Build a sweep of the pyramid

We divide each side of the base in half. We draw a perpendicular, which will be the height of the triangular face. With a circular solution equal to the length of the side face of the pyramid, make a notch on the perpendiculars by placing its foot on the top of the base. Both corners of one side of the base are connected to the resulting point on the perpendicular. As a result, we get a square in the center of the drawing, on the faces of which the triangles are drawn. To fix the model on the side faces, draw auxiliary valves. For reliable fastening, strips of centimeter width are sufficient. The pyramid is ready for assembly.

The final stage of the layout implementation

The resulting pattern of the figure is cut out along the contour. On the lines drawn, bend the paper. Collecting the three-dimensional shape is done by gluing. The provided valves are lubricated with glue and we fix the obtained model.

Development of the quadrilateral pyramid

3D models of complex shapes

After performing a simple polyhedron modelyou can go to more complex geometric shapes. The unfolding of the pyramid is truncated much more complicated in execution. Its bases are similar polyhedra. The sides are trapezoids. The sequence of the work will be the same as the one in which the simple pyramid was made. The sweep will be more cumbersome. To complete the drawing, use a pencil, a compass and a ruler.

Drawing Drawing

The unfolding of the pyramid is truncated inseveral stages. The lateral face of the truncated pyramid is the trapezoid, and the bases are similar polyhedra. Suppose that these are squares. On a sheet of paper, draw a trapezoid drawing with the specified dimensions. The sides of the resulting figure extend to the intersection. As a result, we obtain an isosceles triangle. We measure its side with a compass. On a separate sheet of paper, we construct a circle whose radius is the measured distance.

Deployment of the pyramid truncated

The next stage is the construction of lateral ribs,which has a truncated pyramid. The sweep is performed inside the drawn circle. The bottom base of the trapezium is measured with a circular. On the circle, we mark the five points that connect the lines to its center. We obtain four isosceles triangles. With a circular, measure the side of the trapezium drawn on a separate sheet. This distance is laid on each side of the drawn triangles. We connect the obtained points. The sides of the trapezium are ready. It remains only to draw the upper and lower base of the pyramid. In this case, these polyhedra are squares. To the upper and lower bases of the first trapezium we finish the squares. The drawing shows all the parts that the pyramid has. The sweep is almost ready. It remains only to draw the connecting valves on the sides of the smaller square and one of the faces of the trapezoids.

Completing the simulation

Before gluing a three-dimensional figure,the contour is cut with scissors. Next, the scan is folded neatly along the drawn lines. Fixing the valves to the inside of the model. They are lubricated with glue and pressed against the sides of the pyramid. Models let us dry.

sweep of paper

Making different models of polyhedra

Performing 3D models of geometric shapes- an exciting activity. In order to master it thoroughly, it is necessary to start with the simplest sweeps. Gradually moving from simple crafts to more complex models, you can start creating the most intricate designs.

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