The continuous US (so, not counting the islands and Alaska) and Australia are roughly the same size:
US: 2,959,064.44 square miles (7,663,941.7 km2)
Australia: 2,969,907 sq mi (7,692,024 km2)
And the person above has the impact of the Mercator projection completely backwards: North America and Europe appear much larger than they actually are due to their latitudes. Most notably Greenland looks like it is bigger than Africa! (It isn’t.)
In the picture below, the pale blue is Mercator and the dark blue is actual size:
And here is Africa vs Greenland: