prism. Formulas and properties prism

Defining prism

• prism - a versatile volumetric figure, which consists of two identical flat polygons (foundations), located in two parallel planes, and other facets (side faces) – parallelograms, with common sides of these polygons.

• Fundamentals prism – two faces, which is equal parallel flat polygons (ABCEF, GMNJK).
• Side faces of the prism – all other facets except the basics.
• The side surface of the prism – collection of all side edges of the prism.
• The surface of the prism – a combination of two bases surfaces and side surfaces.
• Side edge prism – common side two side edges.
• Height – is perpendicular, connecting the two bases of the prism at right angles.
• Diagonal prism bases – this segment, connecting two adjacent peaks not, belonging to the same base.
• Diagonal prism side faces – this segment, connecting the two opposing top, lying on one side face but belong to different bases.
• Diagonal prism (AN) – this segment, connecting two vertices, lying on different bases but do not lie on one side.
• diagonal intersection – This intersection prism plane, passing through a prism diagonal bases and side edge. Wedge (at the base of the prism, triangles) has diagonal sections.
• section perpendicular – This intersection prism plane, side edges intersecting at right angle prism.
• Direct prism – this prism, in which all side faces perpendicular to the base. Height is the length of the side edges.
• kidnapped prism – this prism, whose side faces perpendicular to the base.
• Right prism – this prism, which is a regular polygon bases. Right prism can be both direct, so inclined.
• Usіchena prism – this prism, in which two bases are not parallel (Livestock. 2). Truncated prism can be both direct, so inclined.

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prism formulas

The surface area of ​​a prism

formula. Lateral surface area prism through perimeter base and height:S_b = P·h

formula.The surface area of ​​a prism through a footprint, the perimeter of the base and height:S = 2S_AHF + P·h

formula.The surface area of ​​a prism through height (h), length parties (a) and the number of parties (n):

formula. The area right triangular prism consists of two footprint areas and three lateral faces (Livestock. lower) Sпризмы= 2·Sосн+ 3·Sбіч.

Substituting here formula for the area of ​​a rectangle and equilateral triangle area formula and get:

Basic properties prism

• Fundamentals prism – level polygons.
• Side faces of the prism – parallelograms.
• The side edges of the prism parallel and equal to each other.
• Perpendicular cross section perpendicular to all side edges and side edges.
• The height of the straight prism is the length of side edge.
• The height of the inclined prism is always less than the length ribs.
• In direct prism faces can be straight or square.