Question: Using QGIS, if I load a polygon layer and make a new column, how do I fill that column with the:

1. area of each polygon and another column with
2. length of the perimeter of each polygon?

Answer: 
Open field calculator, select the new column and type the following expression

* For area: *$area*
* For perimeter: *$perimeter*

Make sure your layer is in a projected coordinate system (not lat/long ) and in correct units. ( i.e. if your layer's projection has 'meters' as units, your area will be square meters ) Note that reprojecting layers on-the-fly does not change the units for area/perimeter calculation, so you have to first reproject using Save as ... with the correct target CRS.

[![enter image description here](https://i.stack.imgur.com/QF8M7.png)](https://i.stack.imgur.com/QF8M7.png)

[![enter image description here](https://i.stack.imgur.com/qZqUF.png)](https://i.stack.imgur.com/qZqUF.png)
You also can use fTools:
*Vector menu -> Geometry Tools -> Export/Add geometry columns*

It updates your layer automatically by adding AREA and PERIMETER columns.