Why are USGS topographic maps called “quadrangles”?
In the making of topographic maps, the USGS subdivides the United States by using Latitude and Longitude lines to form the boundaries of four-sided figures called “quadrangles”. The maps are often referred to as quadrangle maps (or quad maps).
Different sizes of quadrangles have been used over time, for example the 30-minute quadrangle (30 minutes of latitude or longitude on each side) and the 15-minute quadrangle (15 minutes of latitude or longitude on each side). Since 1947, the primary USGS topographic map size has been the 7.5-minute quadrangle, so each side of the map is bound by 7.5 minutes of latitude and 7.5-minutes of longitude.
USGS 7.5-minute topographic maps covering the contiguous 48 states and Hawaii are published at a scale of 1:24,000, meaning that one inch on the map equals 24,000 inches (2,000 feet) on the ground.
In common use, all of the following terms mean the same thing:
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USGS quadrangle map
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quad map
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7.5-minute quadrangle (or quad or map)
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1:24,000 quadrangle (or quad or map)
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24K quadrangle (or quad or map)
The same would not be true for topographic maps of Alaska. Alaska’s 7.5-minute maps are published at a scale of 1:25,000 (one inch on the map equals 25,000 inches on the ground), so they’re sometimes referred to as 1:25,000 maps or 25K maps.

Learn more:
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Maps for America: cartographic products of the USGS and others