How to approve child items automatically if parent item is approved by reviewer in Sitecore Workflow?
There's no out of the box functionality to approve child items Sitecore, but it is a common enough of a problem.
Basically you would need to write a custom approval action that checks all related items when the main item is approved, and sets the workflow of the related items (or subitems) to approved state.
Here's one example of how this could be done: http://sitecorepromenade.blogspot.com/2015/10/workflow-with-auto-publish-related-items.html
There would be many arguments to implement this feature. How many child items would you want to make the same status as its parent one? Suppose there are many depths of sub items, would you update them as well??
We already implemented customized workflow actions and we are using two options.
If you want to update only page's related items including child item and datasources, you can run the customized workflow action to update its all related items.
If you want to update the workflow status only the parent's child items (doesn't care any related items), we use Powershell script.
Here is my blog and we have updated some classes so far, but the code would be helpful as a starting point. You can check only the code. Sorry for the different language.