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Problem : What is the area of a plane?

A plane extends in all directions without bound--its area is infinite.

Problem : Does the following figure have area?

No. The curve is not closed.

Problem : Does the following figure have area?

Yes. It can be divided into two regions, each bound by a simple closed curve.

Problem : Do intersecting lines have area?

No. Even lines that intersect are still one- dimensional. The intersecting lines do span a plane that has infinite area, but the lines themselves have no area.

Problem : If two figures have the same area, are they exactly the same? Why or why not?

No. Area is independent of shape. Two triangles, for instance, could have the same area, but have three different angle measures, and therefore not be the same.