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A cuboid is a three-dimensional figure bounded by six rectangular surfaces.
Properties of cuboid:
1. The three dimensions of the cuboid are length \((l)\) units, breadth \((b)\) units and height \((h)\) units.
2. It has six rectangular faces.
3. All the vertices are right angle.
4. Opposite sides of the cuboid are parallel and congruent to each other.
Lateral surface area:
\(L. S. A\) \(=\) Area of front side \(+\) Area of back side\(+\) Area of left side\(+\) Area of right side
\(= (l \times h)\) \(+ (l \times h)\) \(+ (b \times h)\) \(+ (b \times h)\)
\(= 2 (l \times h)\) \(+ 2(b \times h)\)
\(= 2 (l \times h\) \(+ b \times h)\)
\(= 2 (l + b)h\)
Lateral surface area of the cuboid \(=\) \(2 (l + b)h\) sq. units.
Total surface area:
\(T. S. A.\) \(=\) Area of top side \(+\) Area of bottom side \(+\) Area of left side \(+\) Area of right side \(+\) Area of front side \(+\) Area of back side
\(= (l \times b)\) \(+ (l \times b)\) \(+ (b \times h)\) \(+ (b\times h)\) \(+ (l \times h)\) \(+ (l \times h)\)
\(= 2(l \times b)\) \(+ 2(b \times h)\) \(+ 2(l \times h)\)
\(= 2(lb + bh + lh)\)
Total surface area of the cuboid \(=\) \(2 (lb + bh + lh)\) sq. units.
The top and bottom area in a cuboid is independent of height. The total area of the top and the bottom is \(2lb\).
Hence \(L. S. A.\) is obtained by removing \(2lb\) from \(2(lb+bh+lh)\).