How big is my property? Can't figure the acreage...

[Merv]

I have a piece of property that is irregular in shape... can't figure out the acreage.. can you help???

Here goes:

1183.71 feet (S88*38'17"W)
1298.69 feet (N28*11'42"W)
688.23 feet (N75*09'20W)
1615.13 feet (N32*55'42"E)
1582.88 feet (N89*34'06"E)
781.70 feet (S00*19'00"E)
494.35 feet (S55*01'00"E)
378.56 feet (S55*01'07"E)
1311.15 feet (S34*57'41"W)
280.72 feet (S00*05'29"E)

I know.. really irregular!! Please help!!!

Thanks,
Merv

[Guest]

I have a piece of property that is irregular in shape... can't figure out the acreage.. can you help???

Here goes:

False Origin,,100 2500,0
A,1183.71 feet (S88*38'17"W),71.87, 1316.62,-101690.64
B,1298.69 feet (N28*11'42"W),1216.46,703.03,-395256.00
C,688.23 feet (N75*09'20W),1392.78,37.77,-867911.66
D,1615.13 feet (N32*55'42"E), 2748.44,915.73,1817929.92
E,1582.88 feet (N89*34'06"E),2760.37,2498.57,4359767.78,
F,781.70 feet (S00*19'00"E),1978.68,2502.89,10237.14
G,494.35 feet (S55*01'00"E),1695.25,2907.92,744026.06
H.378.56 feet (S55*01'07"E)1478.22,3218.09,492154.94
I,1311.15 feet (S34*57'41"W), 403.68,2466.77,-706953.78
J,280.72 feet (S00*05'29"E),122.96,2467.22,117.90
Closure,40.02,125.0047,100.00,2500.00,3654.72
I know.. really irregular!! Please help!!!

Thanks,
Merv

Total area 5356076.39 sq ft, 122.96 acres

Merv, this is a complex problem. I'm glad you included the bearing angles; without them, the problem can't be solved.
I typed a bunch of intermediate answers into the data I quoted to save me retyping, three figures follow each piece of data you gave as comma separated values, and I added the false origin and closure lines. Let me explain my additions.

Each distance and bearing you gave is a vector, basically in polar notation. I can convert it to rectanglular notation (y,x) by multiplying the distance by the cosine and sign of the angle. On maps this is usually called nothing and easting. If the angle begins, with an "S", that is negative northing, and if it ends with a "W", that is negative Easting. The northing and easting can be accumulated to build a table of where the corners are located in a plane. I assigned letters A-J to the vectors you gave

The tail of vector "A" is the origin. However, to keep the whole figure in the NE quadrant, it is assigned a false coordinate of 100' north, 2500' east. This is arbitrary and was chosen after the figure was calculated to get the figure in one quadrant, everything was calculated relative to it.

The first two figures following your data are the northing and easting of the tip or head of vector A relative to its tail at the false origin. The first two figures following each of the other vectors are the northing and easting of the vector head. Vector J should end back at the false origin, but the figure doesn't "close" properly. There is a transcription or surveying error of 40.02 feet, bearing 125.00 degrees, and I assigned a false "closure" side to close the figure. You may wish to check your raw data for typos as the figure should close to much less than a 40' error.

There are several ways to compute the area, the figure could be divided into a bunch of triangles, which would take additional computation of sides, angles then area. It can also be imagined as an upper and lower curve relative to the x axis, The upper curve can be divided into a bunch of trapezoids which are the area between it and the x axis, then the area below the lower half of the curve and axis can be subtracted out. The last figure on each line is the area of the trapezoid represented by that vector, including sign to determine whether the area is included or cast out.

The total area is the sum of those final figures as sq. ft. It is converted to acres by division by 43560 sq. ft/acre.

I have this in a spreadsheet, although I may have made typos in the figures above. Because the figure doesn't close well, please don't expect superb accuracy, but it is probably a reasonable estimate of the area. If you find an error in your raw data, I can easily modify it in my spreadsheet and recompute, or you can recreate the spreadsheet from the description.