platonic solids
TRANSCRIPT
IntGeom12.1.exploringSolids_Prisms.notebook
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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:
Water- Dodecahedron
Fire- Tetrahedron Earth- cube Air- octahedron
Universe- Icosahedron
PLATONIC SOLIDS
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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.
Chapter 12 - Solids
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Types of Solids:
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d.e.
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Cross section: Is the intersection of the plane and the solid. Imagine that the plane is slicing through a solid.
d. e. f.
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Net of a Prism
Net: is the 2-dimensional representation of the faces. (imagine that you unfold the polyhedra.)
** The Surface Area is equal to the Area of the polyhedra's net **
Surface Area: is the sum of the area of the polyhedra's faces.
Lateral Area: is the sum of the areas of its lateral faces.
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Prism: a polyhedron w/ 2congruent faces (bases) that liein parallel planes.
Lateral Faces: are parallelogramsformed by connecting the corresponding vertices of the bases.
Lateral Edges: segments connectingthe vertices and is the intersection of two faces.
Prisms are classified by their bases!!
12.1 Lateral Area, Surface Area and Volume of Prisms
Lateral Area: The sum of the lateral faces.
Total Surface Area: The sum of the Lateral Area and the areas of two Bases.
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Each lateral edge is perpendicular to both bases.
Right Prism
Formula: S.A. of a right prism
S.A. = L.A. + 2B
a= apothemB= area of baseP= perimeter of the baseh= height
L.A. = ph
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Base
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Steps:1. Find the Lateral Area: - Find the perimeter of the Base - Multiply by the height of the prism2. Find the area of 1 Base3. Plug into the formula: TSA = 2B + LA
Find the surface area of the right hexagonal prism.
Base:
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Volume: Bh (area of the Base times the height of the prism)
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Homework:
pg. 478,479: 1-11 (odd), 13-22 (all)