### Theory:

Cube:
Cube is a special type of cuboid whose length, breadth and height are all equal. Properties of cube:
1. Length, breadth and height all are equal.

2. Each edge of the cube is $$a$$ units.

3. It has six square faces.

4. All the vertices are right angle.

5. Opposite sides of the cube 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

$$= (a \times a) + (a \times a) + (a \times a) + (a \times a)$$

$$= a^2 + a^2 + a^2 + a^2$$

$$= 4a^2$$

Lateral surface area of the cube $$= 4a^2$$ 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

$$= (a \times a) + (a \times a) + (a \times a) + (a \times a) + (a \times a) + (a \times a)$$

$$= a^2 + a^2 + a^2 + a^2 + a^2 + a^2$$

$$= 6a^2$$

Total surface area of the cube $$= 6a^2$$ sq. units.

Important!
Total surface area is also called a surface area.