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ELI5 Yahaaa

Counting squares, quickly

Why Do We Multiply to Find Area?

Area counts the squares that cover a shape, and multiplying is just a fast way to count them.

The shape is covered insquaresCount the squares toget areaRows times columnscounts themMeasured in squareunits
Area is a count of squares. Multiplying just counts them faster.

  1. Step 1 of 5

    Area answers how much surface a shape covers.

    The edge How far aroundThe inside How much surface

    It is not about the edge or the width alone. Area asks how much flat space is inside, which is what paint or carpet has to cover.

  2. Step 2 of 5

    Cover the shape in identical squares and count.

    Four squaresacrossThree rows downTwelve squaresin total

    Choose a square unit, tile the shape with it, and count. That count is the area, and nothing more complicated is really going on.

  3. Step 3 of 5

    Multiplying is a shortcut for that counting.

    1 Four in eachrow2×Three rows ofthem310Twelve squares,no counting

    Since every row holds the same number of squares, you can multiply rather than count one by one. The rectangle formula is a counting trick.

  4. Step 4 of 5

    That is why the units are squared.

    Length in metresone directionWidth in metresthe otherdirectionArea in square metressquares counted

    You are counting squares, so the answer is in square metres or square centimetres. The little 2 is a reminder of what was counted.

  5. Step 5 of 5

    Doubling both sides quadruples the area.

    2 m by 3 msix squares4 m by 6 mfour times asmany

    Twice the length and twice the width gives four times the squares, which is why a slightly bigger room needs far more carpet than expected.

    Doubling a pizza's diameter gives four times the pizza, which is why the large is usually far better value than it looks.

The short version

Area counts the squares covering a shape, and multiplying length by width is simply a fast way of doing that count.

Try it yourself

Cover a book with sticky notes in neat rows. Count them, then multiply rows by columns. The two numbers always match.

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