(i) What is the area of the floor
(ii) Area of the celling
(iii) Cost of white washing the walls without doors & windows at the rate of Rs. 12 per sqm
(iv) Cost of polishing both sides of doors and windows at Rs. 7.50/sqm

Explanation

We know,
Area of a rectangular is = \left(length\ \times\ breath\right)

In (i) case,
The length & breath of the room are 6 m & 5 m.
\therefore The area of the floor is =\left(6m\ \times\ 5m\right)
=\ 30\ sqm.

In (ii) case,
The length & breath of the room are 6 m & 5 m.
\therefore The area of the celling is = \left(6m\ \times\ 5m\right)
= 30\ sqm.

In (iii) case,
When we find 4 walls area then the formula is
\rightarrow2\ \times\left(lenght\ \times\ hight\right)\ +\ 2\times\left(breath\ \times\ hight\right) sqm
Or, \{2\ \times\left(length\ +\ breath\right)\ \times\ hight\} sqm
So, the area of 4 walls is = \{2\ \times\ \left(6\ +\ 5\right)\ \times\ 3\} sqm
= \left(2\ \times\ 11\ \times\ 3\right) sqm
= 66 sqm
According to the question,
1 door length & breath is = (2\frac{1}{2}\ \times\ 1\frac{1}{2}) m.
\therefore 1 door area is = (\frac{5}{2}\ \times\ \frac{3}{2}) m
=\ \frac{15}{4} sqm. or 3.75 sqm
And each 3 windows length & breath are = (1.5\ \times\ 1.2) m
\therefore 3 windows total areas are = (1.5\ \times\ 1.2\times3) sqm
=\ 5.4 sqm
\therefore Without door & windows the total area of the walls is
=\{66\ -\ (3.75 + 5.4)\} sqm
=\ (66\ -\ 9.15) sqm
=\ 56.85 sqm
Here, 1 sqm of wall white washing cost = 12 rupees
\therefore\ 56.85 sqm of wall whitewashing cost = (12\ \times\ 56.85) rupees
= 682.20 rupees.

In the (iv) case,
1 door one side area is = 3.75 sqm _{[getting from case (iii)]}
\therefore 1 door both side area is = \left(3.75\ \times\ 2\right) sqm
= 7.5 sqm
Similarly, 3 windows one side areas are = 5.4 sqm _{[getting from case (iii)]}
\therefore 3 windows both side areas are = \left(5.4\ \times\ 2\right) sqm
=\ 10.8 sqm.
So that, both side door & windows total areas are = (7.5\ +\ 10.8) sqm
=\ 18.3 sqm.
According to the question,
1 sqm door & windows polishing cost = 7.50 rupees
\therefore 18.3 sqm door & windows polishing cost = (7.50\ \times\ 18.3) rupees
=\ 137.25 rupees.

Ans: (i) The area of the floor is 30 sqm.
(ii) The area of the celling is 30 sqm.
(iii) Cost of white washing the walls without doors & windows are 754.20 rupees.
(iv) Cost of polishing both sides of doors and windows are 137.25 rupees.