Wedge

Author

Eric W. Weisstein
October 5, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Polyhedra/Wedge.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Wedge.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Initialization

<<Prisms`

Graphic

Show[wedge1=Graphics3D[SolidWedge[{1,.5},.7,0],Boxed->False,ViewPoint->{1.4,-4, .65}]]

Show[wedge2=Graphics3D[SolidWedge[{1,.5},.7,.4],Boxed->False,ViewPoint->{1.4, -4, .65}]]

Show[GraphicsArray[{wedge1,wedge2}]]

Show[GraphicsArray[Graphics[HiddenWireframe[#,ViewPoint->{1.4,-5.5,3},AspectRatio->1.5]]&/@First/@{wedge1,wedge2}]]

LiveGraphics3D

<<LiveGraphics3D`

WriteLiveForm["wedge1.m",wedge1]

WriteLiveForm["wedge2.m",wedge2]

Volume

Oblique

v=Simplify[Integrate[(a-(a-c)z/h) b (h-z)/h,{z,0,h}]]

Right

Simplify[Integrate[a b (h-z)/h,{z,0,h}]]

v/.c->a

Centroid

Oblique

zbar=Simplify[Integrate[z(a-(a-c)z/h) b (h-z)/h,{z,0,h}]]/v

zbar/.c->a