How can I do the same thing Adobe Illustrator?
The problem is that the shape in your AI file is not actually a closed shape, but separate paths, so you can't just change the fill attribute.
You can avoid this by using the Rounded Rectangle tool to make a closed path instead.
- Select the Rounded Rectangle tool
- Click once on the artboard
- Input the settings shown below
- Rotate the shape, and move into position, over the corner of the artboard
- Select the shape and change the fill attribute (circled in red)
Here's a half circle and two separate lines drawn at the ends of the circle. It surely will not get filled with Live paint nor Shape builder, because it's an open shape in the corner of the artboard.
Draw a couple of extra lines or a rectangle to make a closed area:
Then select all and sweep with the shape builder tool over it from top left to bottom right. It get filled with the selected fill color:
A sweep with the Shape builder is needed, if the half circle has a fill. If it's not filled, then a single click inside the wanted new shape is enough
Ungroup the result and delete the unwanted remnants: