Question
Our property has 2 cedar trees on it that were planted in the 1950's. One is 10' away from the street. The city is doing extensive road construction that will likely disturb the ground as close as 5' to the base of the tree, halfway around it. I would hate to lose the tree due to the construction. Should I worry? I am unclear on how the root system is structured.

Answer
The roots of trees extend out about 1 1/2 times the foliage and if more than 25 % of the roots are damaged the crown of the tree will die back on that side. There are fungi that can infect the cut  roots of cedar and over time will kill the tree. If the cut will be 5 feet from the tree and half the way around this will case serious damage to the tree. I am not sure the city will want the tree that close to the roots either. I would speak with the people in charge (maybe the city councilman ) and see if they can protect the roots system and if the tree dies will they reimburse you for the tree.
There are formulas that will give the value of trees. These are based on the species of the tree and the size. and condition. If you want to go this route I would contact the office of the State Forestry Agency and ask one of their Forester to assist you. Most agencies have an Urban Forester on staff that can give the value of the tree.

Here is a web link to one of these value systems.
http://www.na.fs.fed.us/Spfo/pubs/uf/techguide/values.htm