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If you double the side length of a square, how many times bigger is the area of the square? How many times bigger is the area if you triple the side length? What about if the side length is ten times as big or half as big? Generalise this concept for a square of any length. You may wish to express this as a formula for the area of a square in terms of its side length.

Aaliyah
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    What have you tried? Think of a numerical example. Maybe draw some squares on graph paper and count how much bigger the area is when you double a side length. – Dorebell Aug 21 '15 at 04:23

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Notice, the area say $A$ of a square having each side $a$ is given as $$A=(\text{side})^2=a^2$$ now, if side is doubled i.e. $2a$ then area $$A_2=(2a)^2=4a^2=4A=4\times(\text{initial area of square})$$ if side is tripled i.e. $3a$ then area $$A_3=(3a)^2=9a^2=9A=9\times(\text{initial area of square})$$

Thus if the side $a$ of square is increased to $n$ times i.e. $na$ then the area of the square becomes $$A_n=(na)^2=n^2a^2=n^2A=n^2\times(\text{initial area of square})$$

Harish Chandra Rajpoot
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Let $L$ be the length of the square: If you double $L$ you get $2L$ .If you triple $L$ you get $3L$. And so on, but let's not use numbers let's use $S$, so we can generalize all the cases.

Let $S$ be how much you scale up the length of the side of the square. Let $A$ be the area of the square. We know that the area of a square is given by multiplying its side length $(SL)$ by $(SL)$.

$$(SL)^2=(SL)(SL)=(S^2)(L^2)=A$$

But $(L^2)$ is your original area.

Ahmed S. Attaalla
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