Why do you multiply the two sides of the square to get the area?

Answer 1

Areas are measured in squares.

The area of any shape is the number of squares that it covers. The number of squares covered depends upon the size of the squares.

A square centimetre is a square with 1 centimetre along each side.

If you had a square 6 centimetres along each side, how many of these "square centimetres" would be needed to fill its interior?

First, along one edge of the square you could fit 6 of these square centimetres in a row.

You could also fit 6 of these rows down the 6 cm square. So in total there would be 6 x 6 = 36 of the little squares:

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.....|.....|......|.....|......|......|.....|.....

.....|--+--+--+--+--+--|.....

.....|.....|......|.....|......|......|.....|..... In this diagram, each little square is a square with

.....|--+--+--+--+--+--|..... 1 cm along each side.

.....|.....|......|.....|......|......|.....|..... The big square is 6 cm along each side, and you can

.....|--+--+--+--+--+--|..... see the 36 little squares inside it in 6 rows of 6 little

.....|.....|......|.....|......|......|.....|..... squares in each. To count the squares quickly, the

.....|--+--+--+--+--+--|..... sides of the square are multiplied together.

.....|.....|......|.....|......|......|.....|.....

.....|--+--+--+--+--+--|.....

.....|.....|......|.....|......|......|.....|.....

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