I want to color the white area between the red frame and the white triangle. Unfortunately, I don't have a path for that area in order to fill it with color.

In this situation, how can I create a path based on the surrounding paths?

Select everything.
[Edit > Duplicate] or [ctrl+d].
[x] invokes the Shape Builder tool. (There's no toolbar icon. I don't know why.)
Click the area between the triangle and frame.
[enter] to finish.
Apply a fill colour to the new shape.

#1Shape Builder tool, #2Paint Bucket tool, #3multiple boolean operations. 

Duplicating isn't required for shape builder tool. It has a toggle for whether you want to replace/destroy original objects or keep them.

Thank you so much, it works perfectly <3

May I ask what means  "[x] invokes the Shape Builder tool."? What is [x]?

"X" is a hot key

Paddy_CAD

[x] invokes the Shape Builder tool. (There's no toolbar icon. I don't know why.)

Toolbar icon on all my 1.4.2  installs...

Paddy_CAD

There's no toolbar icon. I don't know why.)

The set of tools display in toolbar is configurable. You can choose whether to  show or hide each tool in preferences/interface/toolbar.

karliss

tools display in toolbar is configurable

Thank you. For two years I wondered why there's no shape builder icon. I have no idea how I disabled it.