# A foot is approx. 1/3 of a meter. Why isn’t a sq ft 1/3rd of a sq meter?

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A foot is 0,30m and a sq ft is 0,09m. I know some will say because 0,3 times 0,3 is 0,09 but that wouldn’t explain the break of logic as I perceive it.

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Picture the sizes as literal squares. Start with a square one meter on each side—that’s one square meter. Divide it into thirds both horizontally *and* vertically, so you have three columns and three rows. Each row or column has three squares that are a foot on each side—ergo, nine square feet inside one square meter.

You’re dividing by three twice, once for length and once for height, hence the 1/9th instead of 1/3rd.

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Yes a square meter is technically 10.7639 square feet, not nine, but that’s beside the point being made here.

Areas scale by the square of the distance of a side, while distances scale linearly.

Think about one foot vs. two feet, and the area of a square with sides of one foot vs. two feet. The area of a square with sides of one foot is one square foot, but the area of a square with sides of two feet is four square feet.

When you are talking about square meters you are talking about squares each with a side of a meter. That is obviously going to be more than 3 times that of a square with sides of 1/3 of a meter.

Let’s use yards…

A sq yard is 9 sq feet so 1sq ft is only 1/9th of the area.

(1/3)^2

I hope that makes more sense

You perceive it incorrectly. The first guys answer is right.

1 ft x 1 ft = 1 Sq ft. 3 ft x 3 ft = 9 Sq ft.