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# Calculating sq' of a Property Section?

02/23/2008 10:32 PM

I am negotiating the purchase of additional property from an adjoining property owner.

The agreement is to purchase aprox. 1/2 acre of land between us. Unfortunately, although I know how many sq' are involved, the portion to be acquired has no right angles nor equal sides--I can play with two (2) of the measurements (front & back) to obtain the aprox sq' for a half acre plot, if the two measurements were to be the same. They are not---The front can vary from 2 to 8x the length of the rear ( to be like a wedge of sorts without a point) ----

Can anyone help me with the formula to calculate an area not containing right angles or direct me to the information?

Would appreciate---Donzi

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#1

### Re: calculating sq' of a property section?

02/23/2008 10:37 PM

Hi Donzi,

Try to cut up the parcel of land into a number of triangles and rectangles. Then, make progressively smaller ones until you reach a sufficiently insignificant remainder. Most formulas essentially do this anyway, but in a more sophisticated manner.

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#7

### Re: calculating sq' of a property section?

02/24/2008 6:31 PM

Graebeard

Had considered this method until I reviewed my plot register--The plot had no right angles or equal sides to attach this 1/2 acre section to so I knew I was in trouble trying to use standard rectangle/triangle formulae's and the length 650'+ would make it difficult to physically measure without special equipment.

I appreciate your assistance--PS Found the appropiate formula thanks to another responder --

Thanks again--donzi

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#2

### Re: calculating sq' of a property section?

02/23/2008 11:16 PM

Hi donzi

In SA you must in any case have a qualified surveyor do the subdivision and register the info on the land parcel data. It is therefor the best to get that surveyor to do it for you.

If you want to do it yourselves the method depends on what apparatus you have available.

If you have a theodolite I would set it up in the middle and take successive readings to corner points.

This will leave you with a number of triangles where one angle and the length of 2 sides next to it is known.

accumulate the areas and you have the area.

Note that the area of a triangle must be deducted if the angle of a the next point is in the opposite direction.

If you only have a tape you should measure all the sides of each triangle. Remember area of triangle equal 1/2 base x perpendicular height.

good luck!

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#8

### Re: calculating sq' of a property section?

02/24/2008 6:56 PM

Hendrik

You're right--before it's all over I'll need the services of a surveyor in order to register the land purchase and adjust the property tax papers accordingly with the proper county authorities--I was looking for a quick formula to roughly estimate how the 1/2 acre purchase will enhance this property and ensure that it did not degrade the adjoining property.

Unfortunately I have only a surveyers transit and the points (corners) are over 650' in distance making it difficult to "shoot" without breaking it into smaller sectors.

Another reply has directed me to the appropiate formula for a quadr--whatever--& I should be able to compute with accuracy.

I thank you for your input and i'll record your formula for determining area of triangle for future referance.

Donzi

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#3

### Re: calculating sq' of a property section?

02/24/2008 7:06 AM

Think High School geometry......

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#35

### Re: calculating sq' of a property section?

02/25/2008 4:23 PM

charlie r

that was 55+ yrs ago---

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#36

### Re: calculating sq' of a property section?

02/25/2008 4:58 PM

Well then...hmmm...may require deeper reflection than originally thought necessary!

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#4

### Re: calculating sq' of a property section?

02/24/2008 9:05 AM

The really easy way to do it is to use a CAD program. Almost anyone will work great.

If you don't have access to CAD, use the Trapezium formula if you have four straight sides (most small plots do). If you have to Google trapezium, make sure you get the American form (sides not parallel) rather than the British one (two sides parallel).

Otherwise, make a rectangle and then subtract pieces till you get it.

There's also a standard surveyor's formula but I can't find that book at the moment. You might go to Google Books and look for a surveying book with full view.

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#9

### Re: calculating sq' of a property section?

02/24/2008 7:11 PM

TVP45

Appreciate the info--Did find the formula you indicated--will be able to toggle the front and rear measurements until i have aproximated the 1/2 acre sq footage to the satisfaction of both concerned.

Thanks again--donzi

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#24

### Re: calculating sq' of a property section?

02/25/2008 8:46 AM

Donzi:

You stated twice or thrice that you found the formula to calculate the area of the irregular shapes. If you did, please share with us just don't say you got it. You asked the help and you got it so share with all the participants so other can benefit with it.

Regards;

02252008

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#38

### Re: calculating sq' of a property section?

02/25/2008 5:46 PM

Sorry you didn't get this info (I did post it to a previous reply)--I've noticed many responders are not reviewing previous replies which have said the same thing they are saying and some are reaping the credit (good score) for saying the same thing the first responder was so gracious to offer.

Anyway the site is called "Wikipedia" --It covers many topics so you must toggle through your area of intrest to reach the formula's--Mine was "mathematics" ----"polygon"---"quadrilateral" .

I hope you (and others who may read this) find it intresting.

donzi

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#44

### Re: calculating sq' of a property section?

02/25/2008 7:21 PM

Sorry, I was looking for some equations or formulas.

Once again, thanks.

Regards;

02252008

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#15

### Re: calculating sq' of a property section?

02/24/2008 11:55 PM

CAD is the easiest way to go.

Don't have a CAD program. No problem. Go to the nearest community college that teaches CAD and ask the professor if one of the students could help you out. Just bring along the lengths of each of the perimeter "sides" and an approximate drawing of the shape of the parcel. Approximate angles of the junctions of the "sides" wouldn't hurt but aren't absolutely necessary.

Also, if you or anyone you know has a knowledge of CAD, many community college libraries have the program available in their computer labs. If you talk to them nice, they might give you a temporary account to use the facilities. It doesn't hurt to ask.

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#16

### Re: calculating sq' of a property section?

02/24/2008 11:58 PM

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#5

### Re: calculating sq' of a property section?

02/24/2008 10:37 AM

If the polygon has four sides and the front and back are parallel, i.e. a truncated wedge, then the formula is as follows:

A = (f + b)d/2

where A = area, f = length of front, b = length of back and d = depth from front to back.

If the front and back are not parallel or there are more than four sides, you will find the formula at this site.

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#10

### Re: calculating sq' of a property section?

02/24/2008 7:20 PM

ba/ael:

Unfortunately the front/back legs are not parallel--would have been easy with your formula--However i did find the appropiate formula in the referance material you highlighted for me..

Much appreciate--donzi

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#45

### Re: calculating sq' of a property section?

02/25/2008 10:21 PM

ba/ael:

I want to thank you for answering my question directly (obviously you read the question before you offered your answer)--Since I already had my section plot sheets from the county, I also knew the existing angles/distances/etc.--I only needed the formula since it was impractical to break the plot into geometric parts because of distances, hills .etc.

To tell you the truth, I am overwhelmed and honored that so many took the time to offer their expertise & services to assist on such an insignificant question and I've attempted to thank everyone for their involvement--If I have missed anyone, I apologise in advance..

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#46

### Re: calculating sq' of a property section?

02/25/2008 10:36 PM

donzi,

It always amazes me how the guys at CR4 take the time to answer questions of every sort. I don't know what it is, but I guess they are a special breed.

Your final comment is worth more to me than 20 "good answers". Thank you. Glad I could help.

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#47

### Re: calculating sq' of a property section?

02/25/2008 11:21 PM

yOU'RE WELCOME!--DONZI

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#6

### Re: calculating sq' of a property section?

02/24/2008 5:34 PM

Doesn't it kinda boil down to whether you think it's a good deal or not, regardless of precise square footage?

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#11

### Re: calculating sq' of a property section?

02/24/2008 7:35 PM

Bill

If it wasn't a good deal I wouldn't pursue---It more a matter of ensuring the purchase and the final dimensional configuration does not degrade the adjoining property value &/or dimensional configuration--It can't hurt me! --------Just trying to be a good neighbor!

donzi

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#12

### Re: calculating sq' of a property section?

02/24/2008 10:49 PM

Donzi, There is no formula for irregular shapes. There are two ways I know of to do it. One is simply to break down the total area into sections that you can work with. In other words, be creative and divide it into rectangles and triangles and even if necessary, into semi-circular shapes. Then take the area of each by the normal formulae, and add them all up. Another way is to have the area drawn to scale, and borrow a device called a PLANIMETER, and use that to find the area. It would not be as accurate at the first method, and I don't think you would want to buy a planimeter since they are pretty expensive. Anyway, then divide your answer into 43560 sq ft per acre, and you got it. --jer

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#14

### Re: calculating sq' of a property section?

02/24/2008 11:51 PM

JERRYMACK

THANKS FOR THE REPLY--UNFORTUNATELY THE DISTANCE 650'+ AND THE TERRAIN MAKES IT DIFFICULT TO DIVIDE--HOWEVER I WAS DIRECTED BY ONE OF YOU GOOD PEOPLE TO FORMULA'S THAT APPLY TO MY QUADRILATERIAL (TRAPEZIUM) IN THE "WIKIPEDIA" .

I WILL NOTE THIS LOCATION FOR IT DEFINITIONS OF VARIOUS SHAPES AND APPROPIATE FORMULA'S.

THANKS AGAIN--DONZI

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#17

### Re: calculating sq' of a property section?

02/25/2008 12:02 AM

That will save you walking the perimeter with GPS then connecting the dots (:

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#19

### Re: calculating sq' of a property section?

02/25/2008 12:29 AM

bwire

Thanks--have hand held gps--can't figure out the instructions much less the terminology they use to use it if that makes any sense--even wired them with suggestion to print information to make it user friendly--to no avail!

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#53

### Re: calculating sq' of a property section?

02/27/2008 8:22 PM

Solicit advice of 3.4 gpa 10 year old, as trade off teach them history (:

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#55

### Re: calculating sq' of a property section?

02/28/2008 7:21 AM

Hi, bwire!

Yowch! History? Some kid with a 3.4 average would trade off for that???

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#13

### Re: calculating sq' of a property section?

02/24/2008 11:35 PM

There is no straight formula to calculate, there is a methode....methode of triangle and/or rectangle..

The only way I can see, is to make a draft by yourself on autocad and it will calculate it to you.

I hope you made a good deal with your neighbor after all

Greetings

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#18

### Re: calculating sq' of a property section?

02/25/2008 12:15 AM

Le Noble

You're the second or third responder who's suggested using the "cad" system to calculate my dimentions--My system (computer) is relatively new,has lots of goodies I haven't had time to explore--I wonder if i can access a cad system somewhere to do the calculations--I have the measurements for all four sides or can adjust 2 of the sides until I obtain the 1/2 acre (17k+) sq'.

Intresting--Thanks for the suggestion---donzi

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#28

### Re: calculating sq' of a property section?

02/25/2008 9:58 AM

Donzi,

Send me , in private if you like, the measurements of the four sides of your plot and I will be glad to draw it to you with the suggested split line to get your 17K sq'

or send me in private your IM , (msn, yahoo or skype) we will find a time to do it...

greetings from Lebanon

LE_NOBLE

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#37

### Re: calculating sq' of a property section?

02/25/2008 5:28 PM

Le Noble

Appreciate the offer---"ba/ael" directed me to the appropiate information some replies ago--He directed me to "Wikipedia" which, after defining your area of interest, and toggling through pages of geometric shapes, will eventually disclose the appropiate formula('s).

Again I sincerly appreciate the offer!

donzi

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#49

### Re: calculating sq' of a property section?

02/26/2008 12:07 AM

So, Good luck with your neighbor

curious to know where you did find your formula...

Greetings

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#50

### Re: calculating sq' of a property section?

02/26/2008 7:52 AM

HI Le Noble

Was directed by "ba/ael:" to Wikipedia on the internet--go to mathematics--pologon--quadrilaterial---There is a formula (he gave me) for a poly when two sides are parallel but my plot had to be different so it's more complicated--

Thanks again for the info---donzi

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#20

### Re: calculating sq' of a property section?

02/25/2008 12:53 AM

Can you do the following...

It doesn't seem that hard...

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#21

### Re: calculating sq' of a property section?

02/25/2008 1:55 AM

Your solution is the best, vermin, and actually It doesn't seem that hard...

Area of rectangular = Length x Wide

Area of triangle = 1/2 Base x Height

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#65

### Re: calculating sq' of a property section?

03/19/2008 12:56 PM

What you want is to be able to reliably calculate the internal area of an asymmetrical quadrilateral as defined by the surveyed boundaries of adjacent properties without having to pay for a new property survey.

An Excel(R) spreadsheet can be constructed to do just that, exactly, provided appropriate survey information is available to reliably connect the two adjacent parcels together. I wrote one a few years ago for that same purpose of calculating the area of irregular parcels based on known survey information.

Barring that option, finding someone else to apply their own COGO (coordinate geometry) software to evaluate the area in question may be your most time-wise effective choice.

In any case, good luck with your effort.

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#29

### Re: calculating sq' of a property section?

02/25/2008 10:01 AM

Absolutely a most beautiful answer vermin!

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#39

### Re: calculating sq' of a property section?

02/25/2008 6:19 PM

Johnjohn

You obviously (along with some others) did not look at the firsrt responder (Greybeard) who suggested the same thing (3minutes after i posted).

I'm sure "vermin" appreciated your vote.

thanks--donzi

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#40

### Re: calculating sq' of a property section?

02/25/2008 6:21 PM

vermin

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#41

### Re: calculating sq' of a property section?

02/25/2008 6:43 PM

vermin:

thanks for the input--the distance is over 650'--cant see the front for the back if you know what i mean (hills,trees,etc)--because of this', I asked for the formula to calculate this plot, which is a quadrilateral polygon--I had the measurements for one side (existing) & can toggle the front/rear measurements to establish the "new " side but I couldn't find the formula--as I have noted to others "ba/ael" directed me to "Wikipedia" on the internet--After defining your area of intrest (math) and further "polygon" , etc, formula's are available for numerous geometric shapes.

Thanks again--donzi

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#48

### Re: calculating sq' of a property section?

02/25/2008 11:57 PM

donzi,

You are very welcome!

Good luck,

vermin-

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#54

### Re: calculating sq' of a property section?

02/27/2008 8:24 PM

But circles are fun too...

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#56

### Re: calculating sq' of a property section?

02/28/2008 7:30 AM

Hi, bwire!

Absolutely, circles are fun too. One has only to look at Vermin's appearance to see that!

(BUT... Notice how his eyes wobble up and down at slightly different rates? Do you find that to be as highly suspicious as I do? Think Vermin might be a Martian spy relaying coded information about Earth back to his warrior masters on the red planet? Don't tell anybody I mentioned this, will ya? It's all top secret.)

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#57

### Re: calculating sq' of a property section?

02/29/2008 12:33 AM

Dot dot dash dot dash dash dot squeak dot dot dash...

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#58

### Re: calculating sq' of a property section?

02/29/2008 9:23 PM

Think he's Martian to a different tempo eh?

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#60

### Re: calculating sq' of a property section?

03/03/2008 9:47 PM

Hi, bwire!

Couldn't give this response a 'good answer' rating as I wished to do (since it's off-topic), so I added a blip to the 'off topic' score instead.

Mark

PS. The indefinite code display is a ruse to sidetrack us away from the 'squeak', which contains the code to the eyeball broadcasts. Break the 'squeak' and we've got him!

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#61

### Re: calculating sq' of a property section?

03/04/2008 7:15 AM

ROFLMAO!!! Yeah, vermin is most certainly Martian to the beat of a diff'rent drummer, no matter what planet that animated pocket lint comes from...

Most people don't realize vermin actually glows in the dark, which is a good thing. Makes it harder to sneak up on you at night.

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#62

### Re: calculating sq' of a property section?

03/05/2008 1:17 AM

That's why we wear camo!!!

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#63

### Re: calculating sq' of a property section?

03/05/2008 12:03 PM

So you can drop out of the sky undetected...

...even at sunset...

...pretty sneaky!

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#22

### Re: calculating sq' of a property section?

02/25/2008 4:38 AM

Hi donzi!

• scan the existing plot diagram into your computer,
• convert the drawing into the type used by the cad program,
• specify the measurement units you want the cad program to use,
• copy the drawing into the cad program
• and finally use the cad area calculator to compute the area by simply
• typing the word 'area' into the command prompt and
• clicking on all the points of the part of the drawing whose area you want to know in order around its perimeter.
• When they've all been clicked, hit 'enter' and the area of your drawing will be revealed to you in the command prompt line.

• scan the drawing into a jpeg file and
• send it along to this blogsite and
• precisely one thousand three hundred forty-seven users of the site (give or take the guy fighting the flu) will send you the exact area after calculating it with theirs and post the reults for you.

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#42

### Re: calculating sq' of a property section?

02/25/2008 6:54 PM

MarkTheHandyman:

Thanks--gotta try your directions--if nothin more to see how it works.

donzi

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#51

### Re: calculating sq' of a property section?

02/26/2008 9:44 AM

Hi, donzi!

You're welcome. The problem with a lot of plot drawings is that the angles on the corners are not given on the drawing; and although they are drawn to scale, sometimes the piece of the property that you are interested in has no linear dimensions either. To get the description of the angles, you have to refer to the written plot information that appears on the property's ownership portfolio (deed), or find a copy of that document in the title registry office. And of course, the calculation of the complicated polygons wants to use those angles and dimensions.

So the cad program might be easier to use, since all you have to do is scan it in along with the scale information, and go 'pick, pick, pick, pick, pick, etc. on the outside angles with your mouse snapping the cursor on each; and Bob's your uncle (or Fred, or Bill, with apologies to all). The cad program may also be used to dimension the drawing for you.

Suppose that the piece of land you wanted was a section of the total that hadn't been previously measured or demarcated on any drawings. The owner just said, "Waaal, Bill, you kin have the section from the old well to the corner of the crick over yonder, and back to the road." THAT's the time you throw the drawing into the cad program, draw your lines, and take your dimensions and areas without having to re-hire the transit crew to do it for you.

Mark

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#23

### Re: calculating sq' of a property section?

02/25/2008 7:30 AM

Draw the perimeter of the land/property exactly to a predetermined scale on a sheet of graph paper and then count the whole squares. Then add on the average of the part squares to get the total. Then from the scale, convert the 'squares' to whatever measurement preferred.

In all probability you will not be buying 1/2 acre, more like a plot that happens to be 1/2 an acre. The existing plot boundary of permanent markers (fences, hedges, buildings, roads, rivers etc) will determine the extent of what you think you are buying, and that will set the limits on what you use it for.

The boundary markers might be obvious in your case, but they need to be checked against the deeds of the person selling it. I recall a situation many years ago when a house was purchased with an option on an adjoining 1/2 acre field that was clearly marked in 'red' on the plans, but assumed on the ground by the purchaser (who did not know what an acre looked like) that the red boundary was indicated by the surrounding hedges.

The purchaser then exercised the option and bought the land. Only to find out later that the 'red' field did not extend to the 'far' hedge.

The solicitors denied liability. They blamed the purchaser for not checking the measurements.

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#25

### Re: calculating sq' of a property section?

02/25/2008 8:54 AM

Donzi,

You mention that the area is difficult to measure: had you considered logging into Google earth, locating the parcel of land in question and obtaining a perspective on dimensions from that? In this way you may be able to scale a measurement for the entire plot of land from taking a single dimension and thereafter work out the total area from the satellite picture.

Of course it will suffer from parallax, but, since you are only looking for approximations, perhaps this would work ?

All the best

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#43

### Re: calculating sq' of a property section?

02/25/2008 7:05 PM

zigzag:

Have viewed the property from the satelite view--not very useful at least in my case. I do have something better--the county plot drawings for my section which we're all i really needed if I had know the formula for a polygon--do now---

Thanks---donzi

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#26

### Re: calculating sq' of a property section?

02/25/2008 9:40 AM

Actually, the 'plot on graph paper and count the squares' is a legally acceptable method, dirt cheap, easy to do, and surprisingly precise and repeatable. Been used for centuries. One car get even easier-- cut out the enclosed area, weight it on a precision balance, and then cut out rectangle of same approximate size and weigh it. A simple ratio calculation of weights to (know area of rectangle) yields the unknown area.

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Keith E Bowers, PMP
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#30

### Re: calculating sq' of a property section?

02/25/2008 10:05 AM

Very interesting Keith! <peeps over foxhole rim>

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#27

### Re: calculating sq' of a property section?

02/25/2008 9:47 AM

The easiest thing to do is to hire a registered surveyor. Those guys are really good at Trig. In order to record a deed you'll need a "Legal Description" anyway. You're going to need a surveyor sooner or later and his price should be the same either way.

This answer is based on USA, SC practices.

If you're just looking for a formula, I'll give this to my surveyor and let you know what he says.

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#31

### The easiest way

02/25/2008 11:10 AM

Draw the parcel in Autocad. Then use the area function of Autocad to give you the Area

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#32

### Re: calculating sq' of a property section?

02/25/2008 12:03 PM

If this is redundant, my apologies. 1. Try City or Town Hall for records that may have a plot of the land. Mark out the areas you are interested in, and using the scale shown, measure off the land in questions, and do the same on the actual ground from the plot plan. 2. Go to Google Earth and copy the land as shown, enlarge the area and do the same as above. 3. You can also cut out the area as you see it on the plot, and weigh this area on a good analytical balance vs. a standard square of known area from the same paper, to give you an approximate area of the land in question.

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#33

### Re: calculating sq' of a property section?

02/25/2008 12:05 PM

I suggest drawing this in AutoCad with all of the dimensions and angles.

Then you can just look at the properties and this will give you the exact area within the boundries.

And then you have tis for future use if you do any development on the property.

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#34

### Re: calculating sq' of a property section?

02/25/2008 12:45 PM

The fastest way of finding an area on a plan.

Subdivide the area into triangles.

calculate the area.

a 4 cornered figure can be done with 2 triangle with a common base.

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#59

### Re: calculating sq' of a property section?

03/01/2008 7:56 PM

That would be my suggestion too.

If all four sides are known in length, take the measurement of one diagonal. Your are left with two triangles.

To calculate the area of oblique triangles, you first designate the corners A, B, and C and the opposite sides as a, b, and c in length at random.

Second you find one angle by this formula: cos A = a^2 + b^2 - c^2 / (2*b*c).

Of course, angle A is Acos(a^2 + b^2 - c^2 / (2*b*c) )

From that the area is calculated thus: b * c * sinA / 2. You repeat that for the second triangle and add the results of both triangles for the total area.

If you want to check your result, take the other diagonal distance as well and do the same calculations. The results should be the same.

Regards

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#52

### Re: calculating sq' of a property section?

02/26/2008 10:01 PM

If the coordinates of all of the points are known, vector products are very useful.

You can see in the diagram to the right, a four sided figure with no right angles and no two sides the same.

Point A is taken to be the origin with co-ordinates of (0,0). The units are not specified. They could be feet, yards, meters or any other unit you wish but you must be consistent with the units. Points B, C and D have X and Y coordinates shown in brackets.

The vector product or cross product:

AB x AC = |a b| |c d| (should be written with |c d| below |a b| but the editor will not allow me to do this).

This determinant has a numerical value of (a.d - b.c). This is the area of a parallelogram with adjoining sides AB and AC. The area of triangle ABC is 1/2 AB x AC (hatched red). Similarly, the green hatched area is 1/2 AC x AD or 1/2(c.f - d.e). The area of polygon is thus 1/2(a.d - b.c + c.f - d.e), a very simple formulation.

Additional triangles would be handled in a similar way, so that the area of any irregular polygon can be easily determined if the coordinates of all points are known. I believe that most cad programs use this algorithm to calculate areas of polygons.

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Bruce
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#64

### Re: Calculating sq' of a Property Section?

03/05/2008 3:27 PM

Without seeing the measurements, I would guess you could make up a 0.5 acre plot with a rectangle and a triangle (area = 0.5*base*height) where "base" is perpendicular to "height". Is it more complicated than this?

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