In this problem, make sure to follow the method we use in class to solve problems of centroid. That means, please create a table where each cell corresponds to a variable used in the calculations. Inside each cell, students must not only provide the numerical values but also demonstrate the methodology behind each calculation. For instance, in the case of a rectangle, the table cell for the area should display "height $x$ length," accompanied by the actual numerical values and the proven calculation result within the cell itself. This should be similar to all other existing shapes. Solutions missing the details, or a table will face deductions in grade, even if the numbers are correct. This is important because this will help with clarity and transparency and help me know that you have surely understood the concepts and know the calculations.

Determine the location $(\stackrel{}{x}\frac{,}{b}ar(y))$ of the centroid of the area.