Universal Transverse Mercator projection

[atangopascall]

Please does the UTM projection keep distance and the shape of areas? i would like to know whether 2 areas of a town overlap. so, i have thing to project the areas with UTM but i am not sure if the result areas will keep their shape and surface. If not can you tell me the suitable projection for my work? thanks.

[Azélor]

Let's sum it up.
You want to keep:

Distance
Shape
and area ?

Of course, i'm not THE expert on map projection, but don't think it's possible to keep the 3 criteria on a single projection.
You might be better with a compromise projection like Winkel Tripel that tries to minimize the distortions in general. National Geographic use this as their main projection.

i would like to know whether 2 areas of a town overlap

A town is not that big. No matter the projection, the distortion is marginal.

[Hai-Etlik]

UTM is not a single projection, it's a system of 60 of coordinate systems (projections with a particular measure of distance and an origin) each meant for making large scale (zoomed in) maps of a particular part of the world (a "zone"). It is, as its name says, transverse Mercator which means its Mercator wrapped around the poles rather than the around the equator. Like the normal aspect of Mercator, it preserves angles at the expense of areas. When using the appropriate UTM coordinate system for a zone, it is for most purposes fine to treat it as preserving shape, distance and area.

A town should fit in a UTM zone so as long as you are using the coordinate system for that zone you should be fine.

[Redrobes]

Yes, UTM does preserve most aspects of a map and is a very accurate projection often getting to around about 1mm. If your town crosses the zones in UTM then there will be a huge discontinuity at the boundary. It is often easier to extend one zone beyond the typical UTM zone edge in order to prevent that but the further away from the central zone you are the less accurate it is. The problem is that most coordinate conversion websites and tools for UTM do not allow coords into an extended zone. Therefore, I would not recommend UTM for fantasy mapping but its good for terrestrial / technical maps. You didnt say specifically what your mapping to be more precise about a recommendation. UTM is not all that easy to deal with tho.