When was the idea of area invented?

Before farming was invented, people lived by hunting big animals and finding wild fruits, berries, roots, and edible grasses like wild rice. There are still a few small groups of people who live in this ancient way, which is known as the hunter-gatherer lifestyle. Two such are the San and Kung of the Kalahari desert of South Africa. They are able to live in dry areas where most people would die of thirst in a few days. But they must live in small groups, since they need to gather food from a large area to support just a few families.

About 12,000 years ago, people began to farm because that was a way to get much more food from a small amount of land. One of the oldest known farming towns was Jericho, mentioned in the Bible. Seven thousand years before Joshua arrived, as many as five hundred people lived in Jericho. They grew wheat, barley, peas, and lentils. The picture shows what is left of some ancient houses.

As soon as farming was invented, land area and ownership of land became important. People who had lots of land could have large healthy families. People who had none might have hungry families and go hungry themselves.

To figure out how much to pay for a piece of land, a farmer needs to know how many plants can grow on it. In the diagram at the upper right, there are 6 rows of trees with 10 trees in each row. The total number of trees is 10 + 10 + 10 + 10 + 10 + 10 = 6 tens = 6 * 10 = 60. So the total number of of trees is the number of rows times the number of trees in each row. This is the origin of the formula

Rectangle Area = length times width.

• If instead of small circles we count how many small squares fit into a figure, we come close to the mathematical definition of area. So we can say that the idea of area was probably invented by the farmers of 10,000 years ago.

• Land area has remained valuable from 10,000 years ago till now. Now that we live in cities, the important thing about land is not how many plants you can grow but how many apartments and office buildings you can build on it. We'll do a real-life problem about this kind of area at the end of the unit.

Instructions

• The picture at the upper right shows a rectangular arrangement of trees. Drag the green slider to set its value equal to the number of trees.
• Click 'OK' to check your answer.
• Click 'Another' for a new problem.