Development of the regular many-sided truncated pyramid can be constructed on a certain algorithm. It is enough to consider of it on the example of creation of development of the tetrahedral truncated pyramid in which bases two similar equilateral polygons - a square lie.
It is required to you
- - ruler;
- - pencil;
- - compasses.
Instruction
1. Design side of the tetrahedral truncated pyramid on the plane. You receive a ravnoboky trapeze. The top and lower bases of the constructed trapeze respectively are equal to lengths of edges of the top and lower bases of the truncated pyramid. Sides of a trapeze are equal to lengths of side edges of the truncated pyramid.
2. By means of a ruler and a pencil continue trapeze sides up to crossing. You received an isosceles triangle. Measure by a ruler length of the constructed party of a triangle.
3. On a single sheet draw a circle which radius is equal to the found value. Note a point on a circle. Postpone the piece equal to length of the lower basis of the truncated pyramid from this point. Consistently postpone some more same pieces. Their quantity has to correspond to number of sides of a pyramid. So for a tetrahedral pyramid construct only 4 pieces.
4. Connect the ends of pieces to the center of a circle. You received several isosceles triangles having at least one general party. The quantity of triangles corresponds to number of sides of a pyramid. So for a tetrahedral pyramid they will be 4.
5. Postpone on the parties of triangles from points for circles the pieces equal to length of a side edge of the truncated pyramid. Connect consistently received points. Thus, you constructed the pieces equal on length to the party of the smaller basis of the truncated pyramid. As a result you received development of side sides of the truncated pyramid.
6. Construct the regular polygon equal to the lower basis of the truncated pyramid in the basis of the first trapeze of development. So for the tetrahedral truncated pyramid draw a square, one of the parties of which will coincide with the lower basis of a trapeze. In the same way "attach" the square equal to the top basis of the truncated pyramid. Erase unnecessary pencil lines. Development of the tetrahedral truncated pyramid is ready.