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I have a question:

In general, area of square is Length times Length. If the length is less than $1$ then do we end up with less area?

Like if we have a side whose length is $0.5\mathrm{m}$. Then the area is $0.25 \mathrm{m}^2$. That doesn't make sense to me.

Card_Trick
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MR. Raindrop
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    Let's suppose you have two squares, one of which has sides of one metre, and the other of half a metre. Do you really think the area of the smaller one isn't a quarter of that of the larger one? – Angina Seng Dec 29 '18 at 11:21
  • How many $0.5\mathrm{m}\cdot 0.5\mathrm{m}$ squares fit into a $1\mathrm{m}\cdot 1\mathrm{m}$ squares? The area of the small squares should add up to the large one. – Card_Trick Dec 29 '18 at 11:21
  • @LordSharktheUnknown I have got it now thanks – MR. Raindrop Dec 29 '18 at 11:41
  • $$\frac12\cdot\frac12<\frac12.$$ –  Dec 29 '18 at 11:43

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I believe there is confusion between units of measurement, numeric values and what is being measured. In your example, the side length of $0.5$ m is the same as $500$ mm. As such, the area is also $250000$ mm$^2$. You can't directly compare the $0.5$ of $0.5$ m and the $0.25$ of $0.25$ m$^2$ with each other as the first one is a distance and the second one is an area, just like comparing $500$ mm and $250000$ mm$^2$ doesn't really give you anything. My example shows that the numeric comparison of different types of quantities can be very different depending on your unit of measurement. As the old saying goes, it is like "comparing apples to oranges".

John Omielan
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