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View Full Version : To find area from known perimeter


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