A rectangular bedroom measures 10m by 8m. A square carpet with sides 6m is placed in the room. a) Find the area of the room not covered by the carpet. b) How much did the father pay for the carpet if

The bedroom measures $10 \text{ m}$ by $8 \text{ m}$. The area of a rectangle is given by length $\times$ width.

$$\text{Area of bedroom} = 10 \text{ m} \times 8 \text{ m} = 80 \text{ m}^2$$

The carpet is a square with sides $6 \text{ m}$. The area of a square is given by side $\times$ side.

$$\text{Area of carpet} = 6 \text{ m} \times 6 \text{ m} = 36 \text{ m}^2$$

This is the difference between the area of the bedroom and the area of the carpet.

$$\text{Area not covered} = \text{Area of bedroom} - \text{Area of carpet}$$ $$\text{Area not covered} = 80 \text{ m}^2 - 36 \text{ m}^2 = \boxed{44 \text{ m}^2}$$

The cost per square meter is $550 \text{ ps}$. The total cost is the area of the carpet multiplied by the cost per square meter.

$$\text{Total cost} = \text{Area of carpet} \times \text{Cost per m}^2$$ $$\text{Total cost} = 36 \text{ m}^2 \times 550 \text{ ps/m}^2$$ $$\text{Total cost} = 19800 \text{ ps}$$

The father paid $\boxed{19800 \text{ ps}}$ for the carpet.