Opposite faces of a cuboid are _________ in area.
Solution:
The diagram below explicitly shows the faces of the cuboid which have equal area:
Faces 1 and 2 are equal in area and the area is H × B. These faces are opposite to each other.
Faces 3 and 4 are top and bottom faces and their area is L × B.
Faces 5 and 6 are front and back faces and their area is L × H
Therefore a total of six faces are there in a cuboid with opposite faces equal in area.
✦ Try This: Adjoining faces of a cuboid have ___________ areas.
The diagram below shows the various faces of the cuboid and their adjacent faces.
We know,
Faces 1 and 2 are equal in area and the area is H × B.
Faces 3 and 4 are top and bottom faces and their area is L × B.
Faces 5 and 6 are front and back faces and their area is L × H
Therefore,
Face 1 has adjoining faces 3, 4, 5 & 6 which have different areas from face 1
Similarly,
Face 2 also has adjoining faces 3, 4, 5 & 6 which have different areas from face 2
Face 3 has adjoining faces 1, 2, 5 & 6 which have different areas from face 3
Face 4 also has adjoining faces 1, 2, 5 & 6 which have different areas from face 4
Face 5 has adjoining faces 1, 2, 3 & 4 which have different areas from face 5
Face 6 also has adjoining faces 1, 2, 3 & 4 which have different areas from face 6
Hence we can conclude that adjacent face of a cuboid are different areas.
Adjoining faces of a cuboid have different areas.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Problem 42
Opposite faces of a cuboid are _________ in area.
Summary:
Opposite faces of a cuboid are equal in area
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