Example 2 - Graphical approach
GeoGebra
The graph will show area as a function of base. It can be obtained in two ways: either directly by moving the slider (in this case the table should be disabled) or by plotting the points that correspond to the table (as we normally do in the classroom). Reading the coordinates of point S at its the highest position we get the result.
Here the screencast with the approach shown in GeoGebra is presented.
Solution with TI-Nspire™
              
Other approaches