warm-up assemble platonic solids. unit xi: exploring surface area and volume students will explore...
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![Page 1: Warm-up Assemble Platonic Solids. Unit XI: Exploring Surface Area and Volume Students will explore nets of three dimensional figures. Students will calculate](https://reader036.vdocuments.us/reader036/viewer/2022062804/56649f325503460f94c4ee5a/html5/thumbnails/1.jpg)
Warm-up
• Assemble Platonic Solids
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Unit XI: Exploring Surface Area and Volume
•Students will explore nets of three dimensional figures.
•Students will calculate surface area and volume of solid figures, including composite figures.
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POLYHEDRA (plural for polyhedron)
• A polyhedron is a solid bounded by polygons, called faces, that enclose a single region of space.
• An edge is a line segment formed by the intersection of two faces.
• A vertex is a point where three or more edges meet.
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Am I a Polyhedron?
rectanglesFaces:
Edges:
Vertices:
6
12
8
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Am I a Polyhedron?
rectangles and hexagons
Faces:
Edges:
Vertices:
8
18
12
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Am I a Polyhedron?hexagon and triangles
Faces:
Edges:
Vertices:
7
12
7
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Am I a Polyhedron?
No, it does not have faces that are polygons
![Page 8: Warm-up Assemble Platonic Solids. Unit XI: Exploring Surface Area and Volume Students will explore nets of three dimensional figures. Students will calculate](https://reader036.vdocuments.us/reader036/viewer/2022062804/56649f325503460f94c4ee5a/html5/thumbnails/8.jpg)
Am I a Polyhedron?
No, it does not have faces that are polygons
![Page 9: Warm-up Assemble Platonic Solids. Unit XI: Exploring Surface Area and Volume Students will explore nets of three dimensional figures. Students will calculate](https://reader036.vdocuments.us/reader036/viewer/2022062804/56649f325503460f94c4ee5a/html5/thumbnails/9.jpg)
Am I a Polyhedron?
No, it does not have faces that are polygons
![Page 10: Warm-up Assemble Platonic Solids. Unit XI: Exploring Surface Area and Volume Students will explore nets of three dimensional figures. Students will calculate](https://reader036.vdocuments.us/reader036/viewer/2022062804/56649f325503460f94c4ee5a/html5/thumbnails/10.jpg)
Am I a Polyhedron?
No, it does not have faces that are polygons
![Page 11: Warm-up Assemble Platonic Solids. Unit XI: Exploring Surface Area and Volume Students will explore nets of three dimensional figures. Students will calculate](https://reader036.vdocuments.us/reader036/viewer/2022062804/56649f325503460f94c4ee5a/html5/thumbnails/11.jpg)
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Euler’s Theorem
The number of faces (F), vertices (V), and edges (E) of a polyhedron are related by the formula F + V = E + 2.
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Use the Euler’s Theorem to find the unknown number.
1. Faces: ____ Vertices: 6 Edges: 12
2. Faces: 5 Vertices: ___ Edges: 9
3. Faces: 20 Vertices: 12 Edges: ___
86
30
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Am I a Polyhedron?pentagons
Faces:
Edges:
Vertices:
12
30
€
125• 12( )
€
F +V =E +212 +V =30+212 +V =32V =20
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Faces:
Edges:
Vertices:
8 triangles18 squares
48
€
123• 8 +4 • 18( )
€
F +V =E +226 +V =48+226 +V =50V =24
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Name the number of faces, edges, and vertices of the polyhedron.
Note: This soccer ball has 32 faces, 20 regular hexagons, and 12 pentagons.Faces: 5
€
edges=124 • 3+1• 4( )
=8
€
F +V =E +25+V =8+25+V =10V =5
Faces: 32
€
edges=1220 • 6 +12 • 5( )
=90
€
F +V =E +232 +V =90+232 +V =92V =60
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The Five Platonic Solids - Named after the Greek mathematician
and philosopher Plato
Regular, convex polyhedron with congruent faces of regular polygons and the same number of faces meeting at each vertex.
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Regular (if all of its faces are congruent) Concave and Convex Polyhedra
concaveregularconvex
irregularconvex
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Top View
convex concave
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concave concave
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Your Turn!!!
• A solid has 14 faces; 6 octagons and 8 triangles. How many vertices does it have?
€
12(8 • 6 +3• 8)
1248 +24( )
1272( )
36 edges
€
F +V =E +214 +V =36+214 +V =38V =24