Greetings and welcome to the community forum!

Sorry, there's no "split this in half" operation, but it is possible with just a little extra effort.

The Modify > Shapes > ... approach is the most general, and it can be perfectly accurate if you take the proper steps.

For the general case, dividing any shape, I use two steps: first remove one half and then the other, with two separate operations. Instead of a thin rectangle, I create a shape that completely overlays one half of the shape to be divided.

Here's what the steps look like:

- split_shape.png (3.43 KiB) Viewed 2851 times

1) Polygon tool: draw a closed polygon with at least three vertices. The exact shape doesn't matter.

2) Drag two adjacent vertices to form the cut line. Turn on "snap to object points" to get the vertices positioned perfectly over the square.

3) Extend the ends of the cut line; hold shift while dragging to keep the moving vertex collinear.

4) Select both shapes; copy to clipboard.

__a) Modify > Shapes > Subtract: this leaves the outside half (light blue).

__b) Edit > Paste; Modify > Shapes > Intersect: this leaves the inside half (purple).

This approach can be used with pretty much any shape, although some situations can produce surprising results.

For a square (or rectangle), there's another approach. You can convert the shape to a polygon: Modify > Convert > To polygon, then delete one of the vertices: instant triangle. For the other half, copy the square beforehand, then paste and repeat, deleting the opposite vertex.