can a line segment be drawn on the face of a cuboid
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A (rectangular) cuboid is a closed box which comprises of 3 pairs of rectangular faces that are parallel to each other, and joined at right angles. It is also known as a right rectangular prism. Objects like a wooden box, a matchbox, a tea packet, a chalk box, a dice, a book etc have a similar shape. In fact, all these objects are made of six rectangular planes. This shape is a cuboid. This article is on Surface Area of a Cuboid.
By definition, a cuboid is a closed 3-dimensional geometrical figure bounded by six rectangular plane regions at right angles.

Faces: Cuboid is made up of six rectangles and 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.
Here, adjacent faces are ABCD, ABFE and ABCD, AEHD.
Base and lateral faces: Any face of a cuboid may be called as the base of the cuboid. The four faces which meet the base are called the lateral faces of the cuboid.
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 figure 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.
Cube:
A cuboid having its length, breadth, height all to be equal in measurement is called as a cube. A cube is a solid bounded by six square plane regions, where the side of the cube is called edge.
By definition, a cuboid is a closed 3-dimensional geometrical figure bounded by six rectangular plane regions at right angles.

Faces: Cuboid is made up of six rectangles and 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.
Here, adjacent faces are ABCD, ABFE and ABCD, AEHD.
Base and lateral faces: Any face of a cuboid may be called as the base of the cuboid. The four faces which meet the base are called the lateral faces of the cuboid.
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 figure 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.
Cube:
A cuboid having its length, breadth, height all to be equal in measurement is called as a cube. A cube is a solid bounded by six square plane regions, where the side of the cube is called edge.
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yes of course but line segment should be equal or shorter than the face of a cuboid
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