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Ugyen · Apr 29, 2009, 03:07 AM

I have a problem to find area from a known perimeter of a irregular shape.
For example I have a shape measuring 255m. How much will be the perimeter in meter? Please show me how to calculate the area from this known perimeter?

Perito · Apr 29, 2009, 05:23 AM

No more information? It's not possible to solve. For example, if we assume a plane figure (reasonable, right?), and you were trying to maximize the area, you would choose a circle:

$P = 2 \pi R$

$\frac {255}{2 \pi}=\frac {127.5}{\pi} = R$

$A = \pi R^2$

$A = \pi (\frac {127.5}{\pi})^{2} \approx 5174.5$

On the other hand, let's pick a narrow rectangle of width 1.

$W = 1$

$L = (P-2W) \div 2 = 253 \div 2 = 126.5$

$A = LW = 126.5$

Big difference between 126.5 and 5174.5