CUBOID
In everyday life,
objects like a wooden box, a matchbox, a tea packet, a chalk box, a dice, a
book etc are encountered. All these objects have a similar shape. In fact, all
these objects are made of six rectangular planes. The shape of these objects is
a cuboid.
Cuboid:
A cuboid is a closed
3-dimensional geometrical figure bounded by six rectangular plane regions.
Figure 1
Face – A Cuboid is made up of six rectangles,
each of the rectangle is called the face. In the figure above, ABFE, DAEH,
DCGH, CBFG, ABCD and EFGH are the 6-faces of cuboid. The top face ABCD and
bottom face EFGH form a pair of opposite faces. Similarly, ABFE, DCGH, and
DAEH, CBFG are pairs of opposite faces.
Any two faces other
than the opposite faces are called adjacent faces.
Consider a face ABCD,
the adjacent face to this are ABFE, BCGF, CDHG, and ADHE.
Base and lateral
faces: Any face of a cuboid may be called as the base of the cuboid. The four
faces which are adjacent to the base are called the lateral faces of the
cuboid.
Usually the surface on
which a cube rest on is known to be the base of the cube.
In Figure (1) above,
EFGH represents the base of a cuboid.
Edges – The edge of the cuboid is a line
segment between any two adjacent vertices.
There are 12 edges,
they are AB,AD,AE,HD,HE,HG,GF,GC,FE,FB,EF and CD and the opposite sides of a
rectangle are equal.
Hence, AB=CD=GH=EF, AE=DH=BF=CG
and EH=FG=AD=BC.
Vertex – The point of intersection of the 3
edges of a cuboid is called vertex of a cuboid.
A cuboid has 8
vertices A,B,C,D,E,F, G and H represents vertices of cuboid in fig 1.
By observation, the
twelve edges of a cuboid can be grouped into three groups such that all edges
in one group are equal in length, so there are three distinct groups and the
groups are named as length, breadth and height.
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