# Math question

How do I figure the area of a pool from the perimeter? It is a kidney
shaped (exaggerated) pool.
Steve
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"SteveB" fired this volley in news:1n5vp6-jfb2.ln1 @news.infowest.com:
Use a planimeter to do it, or print a picture of it to some sort of scale on graph paper, then break it up into the smallest polygons (of the same shape and size) you can.
Here's a model of a planimeter in software you can DRAW a picture into.
Also, several CAD programs like Rhino have the capabilities to solve for areas of irregular shapes.
LLoyd
You don't. You need more information.
Divide it into segments - two semicircles for the ends, and groups of triangles or trapezoids for the middle, get their area, and add.
What is it you're trying to accomplish?
Good Luck! Rich
Old-timey method is to take an overhead photo of the whole thing, take a picture of a known area at the same height, cut out both pictures, weigh both pictures, then you can calculate the area of the unknown from the weight. It worked for years for figuring land areas next to rivers that frequently changed course. You can't do it just by measuring the perimeter unless it's a regular figure, circle, semicircle, triangle, hexagon, or whatever.
Stan
And then how do you estimate the volume of water, keeping mind the bottom is curved to the drain.
To figure the surface area having only the perimeter as a known variable.
Steve
Fix a rule to the side of the pool.
Bail out one (or more) 55 gallon drums full from the pool
Area per inch change per drum is approx 88.23 sq ft.
Walk around the perimeter feeling happy :-)
Mark Rand RTFM
Hey, Archimedes, what if a squirrel falls in the pool?
Seriously, that would be fine if it's absolutely dead calm.
What a strange world this is becoming.
Computer power to the people - but you have to be a calculus student or programmer to understand it.
I went through a dozen pages on Google looking for a simple explanation of Simpson's Approximation. But found nothing that did not assume that your could already do integrals (using their software!).
Let me give it a try, Steve.
Working from perimeter alone - on a curved object? That would be tough.
What you are trying to do is come up with an estimate of the area under a curve (integral).
So, we need some dimensions - but how do we measure curves?
That's easy if we break the curves down into a series of rectangles. (Trapaziods work too and would be more accurate, but start square)
Assuming you can measure across the pool...length and width.
Decide on an interval (D). The smaller the interval, the more accurate the answer will be, but the more work you will have to do.
Think of D as the longest Distance involved divided into an even number of pieces. Ten divisions is a good starting point. That makes D be the length divided by 10.
So if the pool is 10 feet long, then D would be 1. Ok so far?
Next, we want the distance across the pool (perpendicular to the long distance).
From that we can easily calculate the area of each rectangle. Refer to these as Area(n).
Now, simply sum the areas.
Volume can be worked similarly, but we'll leave that for next time.
Richard
It is actually simple.
Have a helper on the other end of the pool.
Draw a straight line along the pool.
Start with the edge of the pool.
Go in 1 foot steps along that straight line.
Measure width across the pool perpendicularly to that line, for every such foot step.
Add those widths.
This is the area of the pool in square feet.
It will be relatively accurate.
i
Then you're pretty much out of luck.
A round pool will have a lot more surface area than a long skinny pool with the same perimeter.
Sorry, Rich
In general, you can't. If you kick in the side of a 5 gallon bucket, how much does it hold? The rim length hasn't changed.
In this particular case, call the manufacturer or installer.
jsw
Ig, that's a very good practical solution
Empty some of the oil from one of the 55gal drums onto the water ;-)
Mark Rand RTFM
Thanks. This is basically numerican integration.
i
I suspect that comes from Iggy understanding Calculus and the integral.
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Integrals appear in many practical situations. Consider a swimming pool. If it is rectangular, then from its length, width, and depth we can easily determine the volume of water it can contain (to fill it), the area of its surface (to cover it), and the length of its edge (to rope it). But if it is oval with a rounded bottom, all of these quantities call for integrals. Practical approximations may suffice for such trivial examples, but precision engineering (of any discipline) requires exact and rigorous values for these elements.
My greatest regret in high school is that I didn't wise up and start on the right track to take Calculus.
Wes -- "Additionally as a security officer, I carry a gun to protect government officials but my life isn't worth protecting at home in their eyes." Dick Anthony Heller
Yes. OTOH, there are many other things that I do not know very well. I wanted to try cutting inside thread (6 TPI) and for now I postponed it because I do not know too many things about it to do it.
This newsgroup is a great learning place.
I think that anyone who starts messing with machines, quickly realized that there are great advantages to knowing Descartes coordinate systems, trigonometry, and possibly some calculus. From physics, mechanics and thermodynamics are useful also.
i
Print the plan on a rectangle of paper and glue it on a piece of cardboard the same size. Measure it and find its area. Weigh it as close as you can and find the weight per area.
Cut out the shape and weigh that. Divide that weight by the weight per area to get the area.
The pool area should be less than the area of a circle of the same circumference as the pool perimeter.
Then you better hope you can swim, because no one in their right mind would throw you a life preserver.
Or bail it out and count the gallons and then convert to square feet of water
Gunner
GUNNER'S PRAYER: "God grant me the serenity to accept the people that don't need to get shot, the courage to shoot the people that need shooting and the wisdom to know the difference. And if need be, the skill to get it done before I have to reload."
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