Development of a pyramid is a figure which is formed at consecutive combination of flat elements of a surface with the drawing plane. The pyramid belongs to a many-sided surface, its flat elements are sides in the form of triangles. When performing development of any surface the observance of the basic rules is obligatory: the sizes of all elements have to have full size; the area of the constructed development equals the areas of the developed surface.
It is required to you
- Pencil, ruler, compasses, triangle.
Instruction
1. Example. To construct full development to a trihedral piramidyosnovania of a pyramid – AVS triangle – parallel to the horizontal plane of projections P ₁. Horizontal projection AVS ₁ means it is equal to full size.
2. The side surface of a pyramid consists of the sides having the triangle form. Determine by way of a rectangular triangle the full size of edges of SC and SB. For this purpose on plane P ₂ draw height of a frontal projection of a pyramid of h and designate S point ₀.
3. At right angle to h height from its basis postpone horizontal projections of SC ₁ and SB ₁. In ₀ and With ₀ connect points to S point ₀ – receive SB ₀ and SC ₀ – the full size of edges of SB and SC.
4. AS edge (A₂S ₂, A₁S ₁) is a frontal straight line, so of A₂S ₂ – its full size.
5. Having the true sizes of all sides of a pyramid, construct its development. Postpone AS piece ₀ = AS ₁ on any horizontal straight line. Of a point And ₀ make a notch A₂S radius ₂ (N of century of AS), and of a point With ₀ – a notch SC radius ₀ (N of century of SC), receive S point ₀.
6. ASC triangle ₀ – one of pyramid sides. Complete its adjacent sides. With ₀ make a notch of a point SV radius ₁, and from S point ₀ SB radius ₀ (N of century of SB) – receive a point In ₀.
7. Of a point In ₀ make a notch VA radius ₁, and of S point ₀ – A₂S radius ₂. Note a point And ₀.
8. To direct AC ₀ notches complete the pyramid basis – AVS triangle. It will be full development of this trihedral pyramid.