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
Universe- Icosahedron
Air- octahedron
Water- Dodecahedron
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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 2dimensional shape)
Edge: is a line segment formed by the
intersection of 2 faces.
Vertex: a point where 3 or more edges
meet.
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IntGeom12.1.exploringSolids_Prisms.notebook
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Types of Solids:
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IntGeom12.1.exploringSolids_Prisms.notebook
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e.
d.
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IntGeom12.1.exploringSolids_Prisms.notebook
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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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IntGeom12.1.exploringSolids_Prisms.notebook
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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.
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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!!
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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
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IntGeom12.1.exploringSolids_Prisms.notebook
May 08, 2017
Base
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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
2. Find the area of 1 Base
3. Plug into the formula: TSA = 2B + LA
Base:
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IntGeom12.1.exploringSolids_Prisms.notebook
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Volume: Bh (area of the Base times the height of the prism)
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IntGeom12.1.exploringSolids_Prisms.notebook
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Homework:
pg. 478,479: 1-11 (odd), 13-22 (all)
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