IntGeom12.1.exploringSolids_Prisms.notebook May 08, 2017 PLATONIC SOLIDS They are 5 shapes named after the Greek philosopher Plato. They have the same congruent regular polygon as each face. Each shape will fit perfectly inside a sphere. Every point will touch the sphere! It is speculated that these 5 shapes are the fundamental building blocks of the physical universe. Plato believed that these 5 shapes where the "atoms" of nature and assigned them to the essential elements of nature: Fire- Tetrahedron Earth- cube Air- octahedron Universe- Icosahedron Water- Dodecahedron 1 IntGeom12.1.exploringSolids_Prisms.notebook May 08, 2017 Chapter 12 - Solids Polyhedron: a solid that is bounded by polygons, called faces, that enclose a single region of space. Face: is the side of a solid. (a 2- dimensional shape) Edge: is a line segment formed by the intersection of 2 faces. Vertex: a point where 3 or more edges meet. 2 IntGeom12.1.exploringSolids_Prisms.notebook May 08, 2017 Types of Solids: 3 IntGeom12.1.exploringSolids_Prisms.notebook May 08, 2017 e. d. 4 IntGeom12.1.exploringSolids_Prisms.notebook May 08, 2017 Cross section: Is the intersection of the plane and the solid. Imagine that the plane is slicing through a solid. d. e. f. 5 IntGeom12.1.exploringSolids_Prisms.notebook May 08, 2017 Net of a Prism Net: is the 2-dimensional representation of the faces. (imagine that you unfold the polyhedra.) Surface Area: is the sum of the area of the polyhedra's faces. ** The Surface Area is equal to the Area of the polyhedra's net ** Lateral Area: is the sum of the areas of its lateral faces. 6 IntGeom12.1.exploringSolids_Prisms.notebook May 08, 2017 12.1 Lateral Area, Surface Area and Volume of Prisms Prism: a polyhedron w/ 2 congruent faces (bases) that lie in parallel planes. Lateral Faces: are parallelograms formed by connecting the corresponding vertices of the bases. Lateral Edges: segments connecting the vertices and is the intersection of two faces. Lateral Area: The sum of the lateral faces. Total Surface Area: The sum of the Lateral Area and the areas of two Bases. Prisms are classified by their bases!! 7 IntGeom12.1.exploringSolids_Prisms.notebook May 08, 2017 Right Prism Each lateral edge is perpendicular to both bases. L.A. = ph Formula: S.A. of a right prism S.A. = L.A. + 2B a= apothem B= area of base P= perimeter of the base h= height 8 IntGeom12.1.exploringSolids_Prisms.notebook May 08, 2017 Base 9 IntGeom12.1.exploringSolids_Prisms.notebook May 08, 2017 Find the surface area of the right hexagonal prism. Steps: 1. Find the Lateral Area: - Find the perimeter of the Base - Multiply by the height of the prism Base: 2. Find the area of 1 Base 3. Plug into the formula: TSA = 2B + LA 10 IntGeom12.1.exploringSolids_Prisms.notebook May 08, 2017 Volume: Bh (area of the Base times the height of the prism) 11 IntGeom12.1.exploringSolids_Prisms.notebook May 08, 2017 Homework: pg. 478,479: 1-11 (odd), 13-22 (all) 12.