For this problem, use the following assumptions:

$1$ month $=30$ days

The power company charges you $20$ cents for each kW hr of electricity used.

Solar panels generate electricity for $6$ hours per day $($this accounts for night, bad weather, and the fact that the sunlight hits the panels at less than the optimal angle most of the time$).$

During this $6$ hours per day, assume that every square meter of solar panel has $1000$ W of energy incident on it$,$ from the sunlight.

a$.$ Each month, the power company sends you a bill for an average of $$165$ for the electrical energy you use, which is measured in kilowatt $-$ hours $($kW hr$).$ How much energy does this correspond to each month?

$\_\_\_\_\_\_\_$ kW hr

b$.$ You install a system of solar panels on your roof, aiming to generate $100\%$ of the energy you use in a month. Assuming the panels have an efficiency of $21\%($that is$,$ for every $1$ kW hr of solar energy incident $$on the panels, only $21\%$ can be converted to electrical energy$),$ what area of solar panels do you need to install?

$\_\_\_\_\_\_\_$ m$^2$