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Flat triangles and trapezoids are sometimes used internally by these GPUs as a building block for other polygons, possibly since the logic to split up triangles and quads into flat trapezoids may have taken less die space than a rasterizer capable of handling three edge equations at a time rather than just two.

While exposing these lower level internal primitives typically did not make sense for general purpose graphics accelerators, some in-house embedded implementations did actually go further and only supported flat trapezoids, relying on the CPU to preprocess more complex shapes. For instance, the "SOLO" ASIC used in second-generation WebTV boxes took this approach [1] (among other interesting cost-cutting measures such as operating natively in YUV color space).

[1]: http://wiki.webtv.zone/misc/SOLO1/SOLO1_ASIC_Spec.pdf (warning: 200 MB scan)