Rectangle, square, triangle, trapezoid and others are geometric figures from the section of exact science. A pyramid is a polyhedron. The base of this figure is a polygon, and the side faces of the triangles having a common vertex, or trapezoid. For a complete presentation and study of any geometric object, models 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 sweep. The method of converting flat objects into volumetric polyhedra and certain knowledge from geometry will help to create a layout. It’s not easy to make paper or cardboard sweeps. You will need the ability to execute drawings according to given sizes.
Materials and fixtures
Modeling and performing multifaceted volumetric geometric shapes is an interesting and exciting process. From paper, you can make a large number of various layouts. To work, you will need:
- paper or cardboard;
- scissors;
- pencil;
- ruler;
- compass;
- eraser;
- glue.
Parameter Definition
First of all, we will determine what the pyramid will be. The development of this figure is the basis for the manufacture of three-dimensional figures. Doing work will require extreme precision. If the drawing is incorrect, it will be impossible to assemble the geometric figure. Let's say you need to make a model of a regular triangular pyramid.
Any geometric body has certain properties. This figure has a regular polygon base , and its vertex is projected into its center. An equilateral triangle is chosen as the base . This condition defines the name. The side 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 data of the geometric figure. The parameters of the future model are agreed in advance. The choice of material used depends on these data.
How is a regular pyramid scanned?
The basis of the model is a sheet of paper or cardboard. Work begins with a drawing of the pyramid. The figure is presented in expanded form. A flat image on paper corresponds to pre-selected sizes and options. A regular pyramid has a regular polygon base, and the height passes through its center. We make for starters a simple model. In this case, it is a triangular pyramid. Determine the size of the selected shape.
To build a scan of the pyramid, the base of which is a regular triangle, in the center of the sheet, using a ruler and a pencil, draw the base of the given dimensions. Next to each side we draw the side faces of the pyramid - triangles. Now we proceed to their construction. The dimensions of the sides of the triangles of the side surface are measured by a compass. Put the leg of the compass at the top of the drawn base and make a notch. Repeat the action, moving to the next point of the triangle. The intersection obtained as a result of such actions will determine the vertices of the side faces of the pyramid. We connect them to the base. We get the drawing of the pyramid. For bonding a three-dimensional figure on the sides of the side faces provide valves. We finish small trapezes.
Layout assembly
We cut out the completed pattern with scissors along the contour. Gently bend the scan along all lines. The trapezoid valves are tucked inside the figure so that its faces close. We lubricate them with glue. Thirty minutes later, the glue will dry. Volumetric figure is ready.
Unfolding a quadrangular pyramid
First, imagine what a geometric figure looks like, the layout of which we will produce. The base of the selected pyramid is a quadrangle. Side ribs - triangles. For work, we use the same materials and devices as in the previous version. Drawing is done on paper with a pencil. In the center of the sheet, draw a quad with the selected options.
We divide each side of the base in half. Draw a perpendicular, which will be the height of the triangular face. With a solution of the compass equal to the length of the side face of the pyramid, we do on the perpendiculars of the notch, setting its leg at the top of the base. We connect both corners of one side of the base with the resulting point on the perpendicular. As a result, we get a square in the center of the drawing, on the sides of which triangles are drawn. To fix the model on the side faces, add auxiliary valves. For reliable fastening, strips of a centimeter width are sufficient. The pyramid is ready for assembly.
The final stage of the layout
The resulting pattern is cut out along the contour. We bend the paper along the drawn lines. The volumetric figure is collected by gluing. Lubricate the provided valves with glue and fix the resulting model.
Volumetric models of complex shapes
After completing a simple polyhedron model, you can move on to more complex geometric shapes. Scanning a truncated pyramid is much more difficult to complete. Its bases are similar polyhedrons. Side faces are trapezoidal. The sequence of work will be the same as the one in which the simple pyramid was made. Sweep will be more cumbersome. To perform the drawing using a pencil, pair of compasses and a ruler.
Drawing drawing
Scanning a truncated pyramid is carried out in several stages. The lateral face of the truncated pyramid is a trapezoid, and the bases are similar polyhedrons. Suppose these are squares. On a sheet of paper we carry out a drawing of a trapezoid with the given dimensions. The sides of the resulting figure are extended to the intersection. As a result, we get an isosceles triangle. We measure its side with a compass. On a separate sheet of paper we build a circle whose radius will be the measured distance.
The next stage is the construction of side ribs, which has a truncated pyramid. Sweep is performed inside the drawn circle. The lower base of the trapezoid is measured with a compass. On the circle, we mark five points that connect the lines with its center. We get four isosceles triangles. With a compass we measure the side of the trapezoid drawn on a separate sheet. We lay this distance on each side of the drawn triangles. The resulting points are connected. The lateral sides of the trapezoid are ready. It remains only to draw the upper and lower bases of the pyramid. In this case, these are similar polyhedra - squares. We draw squares to the upper and lower bases of the first trapezoid. The drawing shows all the parts that the pyramid has. The scan is almost ready. It remains only to finish the connecting valves on the sides of the smaller square and one of the faces of the trapezoid.
Simulation completion
Before gluing a three-dimensional figure, the outline is cut with scissors. Next, the scan is neatly bent along the drawn lines. Fixing valves are refilled inside the model. We lubricate them with glue and press them to the faces of the pyramid. Let the models dry.
Making different models of polyhedra
Performing volumetric models of geometric shapes is a fascinating activity. In order to master it thoroughly, you should start by performing the simplest sweeps. Gradually moving from simple crafts to more complex models, you can begin to create the most intricate designs.