11. SurfaceAreaand Volume............................................................................................................
The Polyhedron
LearningObjectives
- Identifypolyhedra.
- Understandthe propertiesof polyhedra.
- Use Euler’s formulasolveproblems.
- Identifyregular(Platonic)polyhedra.
Introduction
In earlierchaptersyou learnedthat apolygonis a two-dimensional(planar)figurethat is madeof threeor
morepointsjoinedtogetherby line segments.Examplesof polygonsincludetriangles,quadrilaterals,pen-
tagons,or octagons.In general,ann-gonis a polygonwithnsides.So a triangleis a 3-gon,or 3-sided
polygon,a pentagonis a5-gon, or 5-sidedpolygon.
You can use polygonsto constructa 3-dimensionalfigurecalledapolyhedron(plural:polyhedra). A
polyhedronis a 3-dimensionalfigurethat is madeup of polygonfaces.A cubeis an exampleof a polyhedron
and its facesare squares(quadrilaterals).
Polyhedronor Not
A polyhedronhas the followingproperties:
- It is a 3-dimensionalfigure.
- It is madeof polygonsand only polygons.Eachpolygonis calledafaceof the polyhedron.
- Polygonfacesjoin togetheralongsegmentscallededges.
- Eachedgejoins exactlytwo faces.
- Edgesmeetin pointscalledvertices.
- Thereare no gapsbetweenedgesor vertices.