### Theory:

Cuboid:
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.

Important!
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 $$2(lb+bh+lh)$$.