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

Steve

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

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.

--

On Wed, 7 Oct 2009 13:10:18 -0600, "SteveB"
wrote:

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

Steve

0.45 x (A+B) x length x average depth x 7.5 = volume (in gallons) of
kidney or irregular-shaped pool
http://www.1paramount.com/poolcare/formulas.php
Google is your friend

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

Steve



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.

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


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

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

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

On Oct 7, 12:10*pm, "SteveB" wrote:
How do I figure the area of a pool from the perimeter? *It is a kidney
shaped (exaggerated) pool.

Steve

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?

http://tinyurl.com/y9h7av5

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

On Oct 7, 1:18*pm, mike wrote:


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

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

http://tinyurl.com/y9cphfy

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

On Oct 7, 12:10 pm, "SteveB" wrote:

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

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.

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.


--
Found--the gene that causes belief in genetic determinism

On Oct 7, 1:44*pm, David Nebenzahl wrote:


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.

Wikipedia says it's Simpson's Rule:

http://en.wikipedia.org/wiki/Simpson's_rule

I never argue with Wikipedia when it agrees with me.

dpb writes:

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

Alone, you don't.

_MINIMUM_ area is that of circle of same circumference, how much
greater depends on the eccentricity.
MAXIMUM not minimum is bounded by a circle

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.


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

Metspitzer writes:

On Wed, 7 Oct 2009 13:10:18 -0600, "SteveB"
wrote:

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

Steve

0.45 x (A+B) x length x average depth x 7.5 = volume (in gallons) of
kidney or irregular-shaped pool
http://www.1paramount.com/poolcare/formulas.php
Google is your friend

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

" writes:

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

Steve



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.

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.

blueman wrote:
.... NO.

Brain fart...

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

--

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

On Oct 7, 12:10 pm, "SteveB" wrote:

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

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.

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.

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

On Oct 7, 3:04*pm, "HeyBub" wrote:
SteveB wrote:
How do I figure the area of a pool from the perimeter? *It is a kidney
shaped (exaggerated) pool.

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

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

On Oct 7, 3:10*pm, "SteveB" wrote:
How do I figure the area of a pool from the perimeter? *It is a kidney
shaped (exaggerated) pool.

Steve

Use SketchUp. It's probably the easiest way.
http://edublog.sedck12.org/.../Calcu...lar_Shapes.pdf

You're welcome!

R

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

Steve


Actually it's a geometry question...

"blueman" wrote in message
...
" writes:

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

Steve



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.

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.

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

Close enough.

Steve

"John H. Holliday" wrote in message
...
"SteveB" wrote in message
...
How do I figure the area of a pool from the perimeter? It is a kidney
shaped (exaggerated) pool.

Steve


Actually it's a geometry question...

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

MikeB wrote:
On Oct 7, 3:04 pm, "HeyBub" wrote:
SteveB wrote:
How do I figure the area of a pool from the perimeter? It is a
kidney shaped (exaggerated) pool.

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

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

First you write the equation for the curve as a function of x: f(x) =
equation.

Area = the integral [from 0 to max x] f(x)dx. Turning the crank gives the
answer.
http://hyperphysics.phy-astr.gsu.edu.../integ.html#c3

An alternative is the Monte Carlo method.

Surround the curve with a box. Generate random points that will land inside
the box. Determine whether each generated point is inside the curve or
outside. If 62% of the random points lie within the curve, the area of the
curve is 62% of the area of the box. Obviously precision grows as a function
of the sheer number of points.

John H. Holliday wrote:
"SteveB" wrote in message
...
How do I figure the area of a pool from the perimeter? It is a
kidney shaped (exaggerated) pool.

Steve


Actually it's a geometry question...

There is no way to figure the area of an irregular, curved object using
plane geometry.

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

Steve


4 bricks and some string to provide a reference rectangle around the
pool, a large pad of graph paper (the 11x17 pads they sell at the art
supply stores are great for this), a tape measure, and about an hour of
time to sketch it out and count the squares. Some chalk to make witness
marks along string path and at edge of pool so you don't lose track of
where you are may be helpful. A framing square may be helpful to ensure
square corners on the rectangle, and good measurements from string to
pool edge. A kid to hold the other end of the tape while you make
measurements would make it go faster.

Yes, all the calculus formulas can probably back into the same answer,
but you would never be sure. For trivial problems, sometimes the
stone-age methods are best.
--
aem sends....

On 10/7/2009 4:21 PM SteveB spake thus:

"John H. Holliday" wrote in message
...

"SteveB" wrote in message
...

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

Actually it's a geometry question...

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

42, of course.

(And it's a calculus question, not geometry.)


--
Found--the gene that causes belief in genetic determinism

HeyBub wrote:
John H. Holliday wrote:
"SteveB" wrote in message
...
How do I figure the area of a pool from the perimeter? It is a
kidney shaped (exaggerated) pool.

Steve

Actually it's a geometry question...

There is no way to figure the area of an irregular, curved object using
plane geometry.



Of course not. That's why we're using fancy geometry.

dpb writes:

blueman wrote:
... NO.

Brain fart...

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

No problem - we all suffer from them - and the older we get, the more
frequent they become, just like real gas

"SteveB" wrote in news:ql5vp6-60b2.ln1
@news.infowest.com:

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

Steve



After all this time you found a use for calculus! :-) But something tells
me you don't have the equation for the perimeter. Just a hunch.

Let's say you were looking at a drawing of the perimeter. If you drew 9
vertical lines you would divide it into 10 approximate rectangles from
which you could figure the approximate area (the ends of the rectangles
are not really square of course) If you divided it into 100 it would be
less approximate and 1000 even more accurate. At a billion-trillion
divisions the unsquare ends of the rectangles become negligible. In
calculus the number of divisions approaches infinity aka: limit as n
approaches infinity.

BFD you say!

Start dividing up rectangles depending on how accurate you need it!

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

Steve



1. Measure the perimeter. Write it down on a scrap of paper. Throw the
paper away.

2. Find your pool on google earth or google maps satellite view.

3. Print it, being sure to include something in the print which is easy
to measure. (deck, section of fencing, etc.)

4. Weigh the print.

5. Carefully cut out the pool. Weigh the pool

6. Using the actual length of the easy to measure object, determine the
area represented by the entire print.

7. Fill in:

mass of pool cutout area of pool (unknown)
------------------- = --------------------
mass of entire print area of entire print


8. Do the math: (mass of pool) * (area of entire print) / (mass of
entire print) = (area of pool)

"HeyBub" wrote in
m:

MikeB wrote:
On Oct 7, 3:04 pm, "HeyBub" wrote:
SteveB wrote:
How do I figure the area of a pool from the perimeter? It is a
kidney shaped (exaggerated) pool.

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

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

First you write the equation for the curve as a function of x: f(x) =
equation.

Little snag here. Has no idea what the equation is. Oh, but there's an
area of mathematics for this too...after differential calculus and after
integral calculus. Crank up the differential equations...mathematical
equations for an unknown functions.


Area = the integral [from 0 to max x] f(x)dx. Turning the crank gives
the answer.
http://hyperphysics.phy-astr.gsu.edu.../integ.html#c3

An alternative is the Monte Carlo method.

Surround the curve with a box. Generate random points that will land
inside the box. Determine whether each generated point is inside the
curve or outside. If 62% of the random points lie within the curve,
the area of the curve is 62% of the area of the box. Obviously
precision grows as a function of the sheer number of points.

Mike Paulsen wrote in news:aQbzm.33634$As.8446
@newsfe13.iad:

HeyBub wrote:
John H. Holliday wrote:
"SteveB" wrote in message
...
How do I figure the area of a pool from the perimeter? It is a
kidney shaped (exaggerated) pool.

Steve

Actually it's a geometry question...

There is no way to figure the area of an irregular, curved object using
plane geometry.



Of course not. That's why we're using fancy geometry.


lol

Red Green wrote in
:

"SteveB" wrote in news:ql5vp6-60b2.ln1
@news.infowest.com:

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

Steve



After all this time you found a use for calculus! :-) But something
tells me you don't have the equation for the perimeter. Just a hunch.

Let's say you were looking at a drawing of the perimeter. If you drew
9 vertical lines you would divide it into 10 approximate rectangles
from which you could figure the approximate area (the ends of the
rectangles are not really square of course) If you divided it into 100
it would be less approximate and 1000 even more accurate. At a
billion-trillion divisions the unsquare ends of the rectangles become
negligible. In calculus the number of divisions approaches infinity
aka: limit as n approaches infinity.

BFD you say!

Start dividing up rectangles depending on how accurate you need it!

p.s. One of the sections of the link that HeyBub posted has some basic
graphics (pictures!) that show what I tried to put into words.

http://hyperphysics.phy-astr.gsu.edu.../integ.html#c4

On Oct 7, 8:52*pm, Red Green wrote:

p.s. *One of the sections of the link that HeyBub posted has some basic
graphics (pictures!) that show what I tried to put into words.

http://hyperphysics.phy-astr.gsu.edu...integ.html#c4- Hide quoted text -

- Show quoted text -

Since the OP doesn't know the formula for the outline of the pool,
he's going to have to stick with simple numerical methods.

See problem #6 in the following link. It shows an
example.

http://tinyurl.com/y9cphfy

You just have to remember to use and even number of "panels".
Simpson's rule, properly done, will end up being more far more
accurate for such a shape than your ability to read the measuring tape
accurately.

RicodJour wrote in :

On Oct 7, 3:10 pm, "SteveB" wrote:
How do I figure the area of a pool from the perimeter? It is a kidney
shaped (exaggerated) pool.

Steve

Use SketchUp. It's probably the easiest way.
http://edublog.sedck12.org/.../Calcu...lar_Shapes.pdf

You're welcome!

R


Without the dot dot dots so the link works.

http://edublog.sedck12.org/media/blo...lar_Shapes.pdf

You're welcome!


Little bit more on it.

http://edublog.sedck12.org/media/blo...rregShapes.pdf

You're welcome!

mike wrote in
:

On Oct 7, 8:52*pm, Red Green wrote:

p.s. *One of the sections of the link that HeyBub posted has some
basic graphics (pictures!) that show what I tried to put into words.

http://hyperphysics.phy-astr.gsu.edu...integ.html#c4- Hide quoted
tex
t -

- Show quoted text -

Since the OP doesn't know the formula for the outline of the pool,
he's going to have to stick with simple numerical methods.

See problem #6 in the following link. It shows an
example.

http://tinyurl.com/y9cphfy

You just have to remember to use and even number of "panels".
Simpson's rule, properly done, will end up being more far more
accurate for such a shape than your ability to read the measuring tape
accurately.




Oh my! Bonus points!! Happy happy, joy joy!

"SteveB" wrote in news:ql5vp6-60b2.ln1
@news.infowest.com:

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

Steve




Looks like from all the replies you're gettin' too much info here Steve.
Here's a simple solution.

Look at perimeter from a distance.
Hold arm straight out with thumb up.
Line up thumb with eye and shape.
Pull number out of your ass...like maybe 42.
Yer dun.

"mike" wrote in message
...
On Oct 7, 8:52 pm, Red Green wrote:

p.s. One of the sections of the link that HeyBub posted has some basic
graphics (pictures!) that show what I tried to put into words.

http://hyperphysics.phy-astr.gsu.edu...integ.html#c4- Hide quoted
text -

- Show quoted text -

Since the OP doesn't know the formula for the outline of the pool,
he's going to have to stick with simple numerical methods.

See problem #6 in the following link. It shows an
example.

http://tinyurl.com/y9cphfy

You just have to remember to use and even number of "panels".
Simpson's rule, properly done, will end up being more far more
accurate for such a shape than your ability to read the measuring tape
accurately.

reply: We do a lot of pools. Some are simple rectangles. Others are
complex, but can be subdivided into geometric forms and simple math solves
for those. It's just when I get one that looks like a blob that I have a
problem. These are done from aerial photos, and once you blow it up so far,
it starts to pixelate, and accurate measurements are no longer possible. I
can get it pretty close with plain math.

Steve

On Oct 8, 12:05*am, Red Green wrote:
RicodJour wrote:
On Oct 7, 3:10 pm, "SteveB" wrote:

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

Steve

Use SketchUp. *It's probably the easiest way.
http://edublog.sedck12.org/.../Calcu...lar_Shapes.pdf

You're welcome! *


Without the dot dot dots so the link works.

http://edublog.sedck12.org/media/blo...lculating_Area...

You're welcome! *

Little bit more on it.

http://edublog.sedck12.org/media/blo...rregShapes.pdf

You're welcome! *

Indeed I am.

I did a "copy link location" since it was a PDF - first time I ever
had an ellipsis swapped in there when I pasted. Remind me to
proofread before I post next time. Thanks in advance!

I'm curious, does anyone else here use Sketchup for determining
areas? I find it amazingly helpful when estimating. It's tailor made
for such things as SteveB is doing. Only a few measurements are
needed and then the curve is tweaked by eye.

R

Red Green wrote:

First you write the equation for the curve as a function of x: f(x) =
equation.

Little snag here. Has no idea what the equation is. Oh, but there's an
area of mathematics for this too...after differential calculus and
after integral calculus. Crank up the differential
equations...mathematical equations for an unknown functions.


Sorry, that's a completely different question. Five cents more, please.

On Oct 7, 8:31*pm, Mike Paulsen wrote:
SteveB wrote:
How do I figure the area of a pool from the perimeter? *It is a kidney
shaped (exaggerated) pool.

Steve

1. Measure the perimeter. Write it down on a scrap of paper. Throw the
paper away.

2. Find your pool on google earth or google maps satellite view.

3. Print it, being sure to include something in the print which is easy
to measure. (deck, section of fencing, etc.)

4. Weigh the print.

5. Carefully cut out the pool. Weigh the pool

6. Using the actual length of the easy to measure object, determine the
area represented by the entire print.

7. Fill in:

mass of pool cutout * * * * area of pool (unknown)
------------------- * *= * * --------------------
mass of entire print * * * *area of entire print

8. Do the math: (mass of pool) * (area of entire print) / (mass of
entire print) = (area of pool)

I like it. Could use a string, stretch it carefully around the pool
edge, measure length, solve for diameter of circle, solve for area.

Harry K

On Oct 7, 7:49*pm, "HeyBub" wrote:
John H. Holliday wrote:
"SteveB" wrote in message
...
How do I figure the area of a pool from the perimeter? *It is a
kidney shaped (exaggerated) pool.

Steve

Actually it's a geometry question...

There is no way to figure the area of an irregular, curved object using
plane geometry.

"plane geometry" is used to find the area of aircraft.