Express the area A of a square as a function of its perimeter. The answer is A=p^2/16?

Question

I would like to express the area ( A ) of a square as a function of its perimeter. My initial attempt led me to the equation ( A = \frac{p^2}{16} ). However, I feel uncertain about my solution. I've tried various approaches to understand this concept, but I'm still struggling. Could someone please explain how to derive the area from the perimeter step by step? Your assistance would be greatly appreciated!

Anonymous · Accepted Answer

If s is the length of the side of the square, then the perimeter (P) is equal to 4*s, so we have:
P = 4s
Solve this for s, giving
s = P / 4
Now the area of a square (A) is equal to the length of the side squares, s^2.
A = s^2
Put in s from what we found above, to get:
A = (P / 4)^2
You can square a fraction by squaring the top and bottom separately, so this becomes:
A = P^2 / 4^2
= P^2 / 16

Estella Cummerata I · Answer

The area of any rectangle can be found by multiplying length by height.  Since length and height are the same in a square, the area of a square is equal to any side multiplied by itself.
The perimeter of a square is four times any side, so A = (p/4)^2
When squaring a fraction, you can square the numerator and denominator separately:
A = p^2 / 4^2 = p^2/16

Anonymous

Express the area A of a square as a function of its perimeter. The answer is A=p^2/16?

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