1

Is there any way to combine these expanded strokes without a completely botched result?

The normal boolean operations aren't working at all.

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2

As I suppose you want to create rectangle with the bent upper right corner.

First of all decompose the problem, think globally. What you see? Not just strokes but rectangle with the bent corner. Corners seems the hardest part to reproduce.

When creating keep in mind to use as little shapes as possible. It will be easier to change them later. In your sketch I counted four shapes (strokes) and aligning them properly is another headache.

Ok, let’s try to reproduce this sketch using only two rectangles.

  1. Make the rectangle with empty fill and desired border width

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  1. Duplicate the rectangle by pressing Cmd + D and decrease duplicated rectangle size by dragging lower left corner.

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  1. After zoom in to small rectangle by pressing Cmd + 2 and hide bigger rect by pressing eye button in the layers list

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  1. Now comes interesting part. We will make bent corner. First enable edit mode on the shape pressing Edit in toolbar enter image description here. Choose left lower corner point and make a round it for e.g. 10 px. At end hit Return (Enter) to finish edit mode.

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  1. It is time to delete two borders (on the right and on the top). Go to menu Layer > Paths > Scissors. Your cursor becomes scissors, hover over right border you will see dotted line over it, click and border will disappear. After delete the upper border as well. Hit return to finish scissors mode.

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  1. Make the first rect visible. Add two guides exactly on the inner edge of bent corner. Guides will help us to cut upper right corner of bigger rect properly.

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  1. Select bigger rect, enable edit mode add two points on upper and right borders. Position of the points you can get from guide positions or they will snap to guides automatically while dragging them. Make them straight in the inspector panel.

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  1. Select upper right point of the bigger rect in edit mode and delete it.

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  1. Brace yourself, end is coming! Select two rects and press Union enter image description here on toolbar menu. You will see something like that

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  1. Expand result layer in layers panel. In front of first layer you will see small grey intersected squares, click on them, in the drop down menu select None.

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  1. You will notice bent corner is not in aligned properly. Just select it and move to the right and up exactly to border-width/2 amount. In my case border width = 4 px, so move by 2 px.

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  1. Voila! We are done with nice and properly aligned object with only two shapes.

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Now it is not a problem to change border width and border color.

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At first sight it looks complicated but it takes me about 30 seconds to go through these steps. Just practice a lot.

Sketch file.

Homework: Try to make rectangle with 2, 3, 4 bent corners.

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