Module 4 Polyhedron PDF

People MODULE 4 POLYHEDRON DEFINITION: A solid bounded by planes is called POLYHEDRON. The intersection of the planes which bound a polyhedron is called edges; the intersection of the edges are called People vertices; and the portions of the planes included by its edges are c...

People MODULE 4 POLYHEDRON DEFINITION: A solid bounded by planes is called POLYHEDRON. The intersection of the planes which bound a polyhedron is called edges; the intersection of the edges are called People vertices; and the portions of the planes included by its edges are called its faces. The surfaces on the sides of polyhedron are called lateral faces and their intersections are called lateral edges. The line joining any two vertices of a polyhedron, not on the same face, is called a diagonal of the polyhedron. If the section made by a plane cutting a polyhedron is convex polygon, the solid is called a convex polyhedron. People Polyhedrons are classified according to the number of its faces People POLYHEDRON Number of faces tetrahedron 4 hexahedron 6 octahedron 8 dodecahedron 12 icosahedron 20 People PRISM A polyhedron two of whose faces are equal polygons, which lie in parallel planes and have their homologous sides parallel, and whose other faces are parallelograms, is called prism. People Parts: Bases- the two equal and parallel faces Lateral faces- the other faces Lateral edges- intersection of the lateral faces Lateral edge Lateral surface- sum of all the lateral faces Lateral area- sum of the areas of the altitude lateral faces Altitude- the perpendicular distance between the bases of a prism Prisms are named according to their bases Triangular prism Rectangular prism Pentagonal prism Hexagonal prism A prism whose lateral edges are perpendicular to the bases is called right prism. A prism whose lateral edges are not perpendicular to the bases is called an oblique prism. A right prism whose bases are regular polygons is called regular prism. A section of a prism made by a plane perpendicular to its lateral edges is called right section. The part of a prism included between one base and a section made by a plane oblique to that base, and cutting all the lateral edges, is called truncated prism. A prism whose bases are parallelograms is called parallelepiped. A parallelepiped whose lateral edges are perpendicular to its bases is called a right parallelepiped. A parallelepiped all six of whose faces are rectangles is called rectangular parallelepiped. A parallelepiped whose six faces are all squares is called cube. A parallelepiped whose lateral edges are perpendicular to its bases is called a right parallelepiped. The quantity of space enclosed by the surfaces which bound a solid is called volume of the solid. Important Properties: The lateral faces of a prism are either rectangles or parallelograms.If each base of a right prism is regular polygon of n sides, the prism contains n number of congruent lateral faces which are rectangles The sections of a prism made by parallel planes intersecting all the lateral edges are congruent polygons. The bases of a prism are congruent polygons. Every section made by a plane parallel to the base is congruent to the base. The lateral edges of a prism are parallel and equal. CUBE A cube is a polyhedron whose faces are all squares. Properties The three dimensions of a cube are equal to each other. That is, all edges are equal. All the faces of a cube are congruent squares. Formulas: Area of a face = l x w A = e2 Lateral area S = 4e2 e Total area= 6(area of one face) T = 6 e2 Volume = (EDGE)3 V= e3 e e Exercises 1. A glass factory has an order for 1000 glass paper weights. Each is to be in the form of a cube. If this order requires 8000 cu. In. of glass what is the total surface are of one of the paper weights? 2. A cube of edge a is cut by a plane containing two diagonally opposite edges of the cube. Find the area of the section. 3. Find the length of the diagonal of the cube whose side is a. 4. How much material was used in the manufacture of 21,000 celluloid dice, if each has an edge of ¼ in? 5. Find the volume and the total are of the largest cube of wood that can be cut from a log of circular cross section whose radius is 12 in.