Rock Island Trail Greenwood Connector - Route 1P (primary, mostly paved) SOUTH - Primary suggested Greenwood Connector route (shortest and best access to water, convenience stores, mostly paved--but several blocks of higher traffic roads in Greenwood compared with the RIGC-1L route, which is longer but lower traffic, and more pavement compared with the RIGC-1G route).
The Rock Island/Katy Trail system in Missouri stretches over 300 miles across the state. But there is a short 11-mile gap in the trail between Lee's Summit and Pleasant Hill.
This map has directions for a low-traffic road route to bridge that gap in the southeast direction--Lee's Summit to Pleasant Hill.
Note that this route takes you past two parks (restrooms in the Summer - water at Liberty Park Greenwood may be on year around) and a convenience store in Greenwood.
This route is almost all paved - except for one short, relatively smooth, gravel section south of Greenwood, about 1/2 mile in length. This gravel section should be no trouble at all if you are equipped to ride a trail like the Rock Island.
Unfortunately there is no 100% paved route between Lee's Summit and Pleasant Hill that is also reasonable for bicycling. So this is your best option if you prefer a fully paved route.
The route has one convenience store (Caseys in Greenwood - generally open 7am-11pm) and one location where you should be able to find water all year around (Liberty Park in Pleasant Hill). Allendale Lake Park in Greenwood has restrooms, though they are open only in good-weather months.
If you want to more completely avoid traffic, you can try the L (longer) route - RIGC-1L. If you want some more gravel, and a little more scenic route or G (gravel) route option - RIGC-1G.
More information: mobikefed.org/2019/04/369-miles-connected-trail-across-missouri-new-rock-islandkaty-trail-connections-maps-routes-