Switzerland is about 13 times smaller than Yemen.

Yemen is approximately 527,968 sq km, while Switzerland is approximately 41,277 sq km, making Switzerland 7.82% the size of Yemen. Meanwhile, the population of Yemen is ~31.0 million people (22.5 million fewer people live in Switzerland).
Tip: This to-scale comparison of Yemen vs. Switzerland uses the Mercator projection, which distorts the size of regions near the poles.
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