(from Cambridge Dictionary of American English)

swath
noun [C]
a strip or belt, or a long area of something
The sheriff's department polices a wide swath of the county.

swathe was not found in the Cambridge Dictionary of American English

swath (swth, swôth) also swathe (swth, swôth, swth)
n.

The width of a scythe stroke or a mowing-machine blade.
A path of this width made in mowing.
The mown grass or grain lying on such a path.
Something likened to a swath; a strip.

Idiom:
cut a swath
To create a great stir, impression, or display: “He cut a bold and even sacrificial swath across American politics” (Gail Sheehy).
To extend in distinctive physical length and width: “the surprising 17th Arrondissement, which cuts a generous swath across northwest Paris” (Jean Rafferty).
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[Middle English swathe, from Old English swæth, track.]
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Source: The American Heritage® Dictionary of the English Language, Fourth Edition
Well, CapK, we are both right, it seems. Once again, it depends which side of the pond you're on. Lucky you, if Hurricane Consuelo veers off into the ocean, she's likely to lose all her strength before reaching Merry Olde and you.