If you have a good TimeMachine backup you should be able to delete the current partitions and then reformat the drive with a fresh partition. But you'll need to create a boot disk to do this right. So you'll need a 16 GB USB thumb drive then from a working Mac follow this guide: How to create a bootable macOS Sierra installer drive
Then boot up using your install drive. When you here the Bong, Press the Option key to get to the Boot manager so you can select the USB drive. But before you run the installer, run Disk Utility to test the drive (Disk First Aid) again and then delete the partitions. The OS installer will setup the partitions for you and install the newer system firmware so you can gain Internet recovery services.
Once the OS is installed (it may take a bit of time so I would start it up and let it be for the night) see if the partitions are correctly sized. Then do your TimeMachine restore. If not your drive may need to be replaced.
Be careful here, as your system uses a special drive which has an internal thermal sensor configured per Apples specs so you'll need to use this: OWC In-line Digital Thermal Sensor for iMac 2011 Hard Drive Upgrade which replaces the internal with an external sensor so you can use any HD or even a SSD! Here's the IFIXIT guide you'll need to follow: iMac Intel 27" EMC 2429 Hard Drive Replacement