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Perimeter

Perimeter is the length of the boundary of a two-dimensional figure. You might picture it as the distance an ant would travel if it were to start at some point on the edge of the figure, and crawl the entire way around the figure, along the edge, until it reaches its starting point

Differentiating the meaning from area

Here is a picture of a six-sided figure, and two illustrations that show what is meant by the "boundary" and "interior" of that figure. Those words --- boundary and interior --- are used in mathematics pretty much the way they would be used in geography.

Image:PerimeterArea.png

The perimeter of a figure is the (one-dimensional) measure of the boundary of a figure. It is a length that might be expressed just as a pure number (like 7 or 12), or with units (e.g., 7 miles, 12 inches, 0.7 centimeters). The area of a figure is the (two-dimensional) measure of the "interior" (the inside) of that figure, the amount of "stuff" it is made of. It, too, may be expressed as a pure number (without unit). It can also be expressed using units associated only with area (there aren't many, but "acres" is one), or with "square units" related to the units that are used to measure the perimeter (e.g., square miles, square feet, square meters.)

Circumference

Circumference is just a special name given to the "perimeter" of a circle. The meaning is exactly the same as the meaning of perimeter: the distance around the figure (in this case, a circle). The area of a circle gets no special name: area is used for any two dimensional figure.

What's in a word?

The peri- in perimeter means "around" or "enclosing." The meter is used in many words that suggest measuring, like thermometer (measures temperature), diameter (measurement across the center of a circle), barometer (measures weight), and, of course, meter. So, perimeter is the "measurement around" a figure.