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Area puzzle

What fraction of the total area in this diagram is shaded?

Slide for the answer.
The solution I implemented above uses a few shear transformations to make it easier to find the areas of the triangles. For more about shear transformations, see https://www.geogebra.org/m/yZQNWxs6.
I got this problem from Twitter. Thanks to Catriona Agg. https://twitter.com/Cshearer41/status/1646814725240487937