Using Draftsight to find area of scanned images

Hello, taking engineering hydrology and have no experience with drafting. Our professor told us to use this program to find the area of scanned images, pretend watersheds in different shapes that he hands out on worksheets. We have "watersheds" that are polygons or rounded shapes. We have different methods to determine average rainfall if some data points are known across the region. One of the methods involves drawing smaller polygons (thiessen method) around each data point in the polygon or rounded watershed and then determining the overall area of the watershed  and the area of each smaller area for the data point to make a weighted average. Another method breaks up the watersheds into smaller areas using contour lines from rainfall data (isohyetal method). So basically I have a printout of an area which I then make smaller areas inside and I need to find all the areas. Some are polygons with straight edges but some are rounded. Also when I use the contour method the inside smaller areas are always rounded. How can I use draftsight to scan these images and then determine all these areas. Thank you.