First off, I basically stole this from @NatBanting. And when I say “basically”, I mean “entirely.” Here’s the original blog post where you can see his frustratingly boob-shaped backyard. I tried to video my backyard but I didn’t have a good ladder to get a good vantage point. And my roof is terrifyingly steep. And I’m scared of heights. So I let him do the grunt work and I sat back and tried to figure out Geogebra on the fly. I’ve used Geogebra before, but not quite in this capacity, and to this degree. Huge thanks to John Golden (@mathhombre) for his Geogebra session in Grand Rapids a few months ago for encouraging us to create and share. I created the shape of the yard using inkscape (inkscape.org).
Now, I have a sprinkler system, rather than a hook-up-to-the-hose kind of sprinkler. So once you place them in the ground, you’re sort of stuck. Therefore, it’s much more imperative that you place your sprinkler heads correctly to minimize the amount of water overlap and the sprinkler cost and maximize the amount of water coverage. That’s what this task is intended to do.
=======
Geogebratube: Sprinkler task
=======
As for facilitating a task like this, I’d consider having students attempt this using paper and pencil first, make predictions, share their work, before giving them this Geogebra worksheet. In fact, you could start with Nat’s original post using a mobile sprinkler, then throw in the installation of the sprinkler system as an extension (or twist).
Also, you could easily modify this task with several different yard shapes (possibly by someone who isn’t afraid of heights). You could also scaffold nicely by starting off with just the 360 sprinklers and then slowly bringing in the sector sprinklers. If you want to go crazy, you could extend this into a project with PVC pipe distance and such.
How would you use or modify this task for your classroom? Let everyone know in the comments!
=====================================
Epilogue: It Takes A Village (To Develop Curriculum)
This is curriculum-creation in the 21st Century: Nat created the task. John taught me how to better use Geogebra. I just took their stuff and ran with it. This may warrant an entire blog post, but for now, I just wanted to highlight this.
emergent math 
I’m liking this activity, but would add an element where students grade the works of other groups and analyze them for waste: overlap between spray radii. Always fun to add constraints, like cost per hose or PVC, just to keep kids thinking.
That’s a great call, Bob. I’m a huge fan of students analyzing their peers’ work. That could certainly go in between the on-paper investigation and the Geogebra exploration, and then again at the end.