周辺 and 周囲: a surrounding area and a perimeter
Compare finding an area around a station with measuring around an object, keeping perimeter length separate from area.
The area around a point
周辺, read しゅうへん, names an area around a point. 駅周辺の地図を見ています。 says that someone is looking at a map of the station area.
工事現場の周辺では音が聞こえます。 says that sounds can be heard around the construction site. It does not require being inside the site.
Surroundings or the line around an object
周囲, read しゅうい, can name surroundings or a perimeter. 池の周囲を歩きました。 says that someone walked around the pond.
柱の周囲を測りました。 says that the column’s circumference was measured. In this measurement context, it does not mean the area of surrounding land.
Area information and length measurement
建物の周辺 and 建物の周囲 may overlap for surrounding locations. In 周囲が二メートルです。, check the object whose perimeter is being measured.
周囲の状況を確認してから動いてください。 asks someone to check the surroundings before moving. Keep checking before movement.
Does 柱の周囲を測りました。 mean measuring the floor area occupied by the column?
Show the answer and why
No. Here it describes measuring the length around the column.