Math question

How do I figure the area of a pool from the perimeter? It is a kidney shaped (exaggerated) pool.

Steve

Reply to
SteveB
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Alone, you don't.

_MINIMUM_ area is that of circle of same circumference, how much greater depends on the eccentricity.

Example of magnitude difference depending on shape, multiplier is pi for a circle, 4 for a square of the same "radius" so square would bound 4/pi

--> ~33% greater area.

Reply to
dpb

0.45 x (A+B) x length x average depth x 7.5 = volume (in gallons) of kidney or irregular-shaped pool
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Reply to
Metspitzer

How critical is the measurement? I would sketch out the length and width, cut off triangles for the belly of the kidney and outside the curves....area of the rectangle less the areas (roughly triangular) outside of the curves should give a fairly close measurement.

Reply to
norminn

You can't. That's what Integral Calculus is for.

Reply to
HeyBub

You can estimate the area by overlaying the circumference of a couple of circles, figuring the area of each, then adding those areas together. Take the remaining area not covered by your circles, and estimate that area, adding it to the previous area to obtain your final rough estimate.

Jon

Reply to
Jon Danniken

If accuracy is important, I'd use the Simpson's Rule formula, where you take measurements across the pool at interals and plug those distances into the formula. You also have to plug the interval distance into the formula.

Why do you ask?

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The hard part is Googling a web page that presents the formula in an easy to understand manner for novices.

Reply to
mike

Found something. See problem #6 in the following link. It shows an example without too much math jargon

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Reply to
mike

On 10/7/2009 1:18 PM mike spake thus:

Ackshooly, that's called "Simpson's approximation", but yes, it does work as you described. It's a weighted-average method of approximating the area under a curve.

Reply to
David Nebenzahl

Wikipedia says it's Simpson's Rule:

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I never argue with Wikipedia when it agrees with me.

Reply to
mike

MAXIMUM not minimum is bounded by a circle

NO. Circle has area: pi * r^2 and perimeter 2*pi*r so multiplier is r/2

And a square with equivalent perimeter has area: pi^2 * r^2/4 So square is pi/4 as large - or about 22% SMALLER than a circle with equivalent perimeter

Reply to
blueman

The OP asked for AREA not volume in gallons. Also your formula at best is some vague type of approximation since there is no standard kidney-shape and certainly irregular-shaped is even less well-defined. Although since the site doesn't define what A and B are, the formula will by definition be true for some values of A and B ;)

Reply to
blueman

This is probably the best simple way if an approximation is OK. You can get as precise as you want by making the sketch more precise and projecting it on a fine grid and counting the "squares" and fractions of "squares" covered by the pool.

Reply to
blueman

blueman wrote: ...> NO.

Brain fart... :(

circle has minimum perimeter for given area, and i turned it around w/o thinking....

--

Reply to
dpb

And, as delta-x approaches zero, you get the integral.

Reply to
HeyBub

So what is the formula then, or how would one use integral calculus to derive the area of the pool?

Reply to
MikeB

Use SketchUp. It's probably the easiest way.

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You're welcome! ;)

R
Reply to
RicodJour

Actually it's a geometry question...

Reply to
John H. Holliday

For my use, I took four widths, averaged them, then multiplied by the length.

Close enough.

Steve

Reply to
SteveB

And the answer is ...................?

Reply to
SteveB

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