410File 3 Area Coordinates Blackboard

8/13/2019 410File 3 Area Coordinates Blackboard

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ITCM 410 - Construction Surveying

File #2Topographic

SurveyingArea Computation


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Area Units

Units :

ft2, mi 2, m 2, km 21 acre = 43,560 ft 2

640 acres = 1 mi2

10,000 m 2 = 1 hectare = 2.47 Acres


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Area Field Measurement

Division into simple figures(triangles, rectangles)

Offset from a straight lineDouble Meridian Distance(DMD)

Coordinates


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Area by Division Into Triangles

A track can be divided into simplegeometric figures.


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Area of a Triangle(when sides are known)

where: a , b , and c are sides of the triangle s = ( a +b +c )

Another formula for area of a triangle isArea = ab sin C

where: C = angle included between side a and b.

))()(( c sb sa s s Area


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Area by Division Into Triangles

The area of a parcel is the sum of theareas of all triangles. The choice ofwhich equation to use will depend onavailable equipment. If an EDM isaccessible, lengths of triangle sides arereadily measured and first equation is

best. If 2 nd equation is used, bothangles and distances must bemeasured.


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Area By Offsets

Irregular tracts can be reduced to series oftrapezoids by right-angle offsets from

points at regular intervals along measuredstraight line.


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Area By Offsets

where: b is the length of a common interval between offsets and h are the offset


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Area By Offsets

Area = 50[(0 + 5.2 + 8.7 + 9.2 + 4.9 + 10.4+ 5.2 + 12.2 + 2.8)/2]= 2860 ft 2


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Area By Offset for a Tract With

Curved Boundary


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Area - Curved Boundary

For irregular curved boundaries, the spacingof offsets along the reference line should beselected so that connecting straight lines ona curved boundary at offset pointsaccurately define the curves.


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Area - Curved Boundary

Area= [60(7.2+11.9)+80(11.9+14.4)+100(14.4+6.0)+30(6.0+6.1)+105

(6.1+11. 8)+60(11.8+12.4)]= 4,492 ft


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Area Map Measurement

Division of AreaCoordinate Squares

PlanimeterComputer software


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Area Map Measurement


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Area by Coordinates


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Example


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Area by Coordinates


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Area by Coordinates


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Area by Coordinates

Sum the productsof diagonal termsupward to theright:

(1,371.35 734.98) +(691.17 908.98) +(100.00 239.96) +

(208.89 100.00) +(1,169.72 857.00) =

= 2,683,510


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Area by Coordinates

Sum the productof diagonal termsdownward to theright:

(857.00 691.17) +(734.98 100.00) +(908.98 208.89) +

(239.96 1,169.7) +(100.00 1,371.35) =

= 1,273,529


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Area by Coordinates

Determine the double area by taking thedifference between the two sums:

2,683,510 - 1,273,529 = 1,409,981 Divide the double area by 2:Area = 1,409,981 2 = 704,991 ft

Divide by 43,560 ft/ac:Area = 704,991/43,560=16.18 acres


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Area by Coordinates Method

Deg Min Sec Latitude Departure Latitude Departure Northing Easting A 5000.00 5000.00

126 56 10 S 53 o 04' E 323.626 -194.4744 258.6758 -194.4647 258.6601B 4805.54 5258.66

178 20 30 S 1 o 40' E 101.517 -101.4740 2.9378 -101.4710 2.9329C 4704.06 5261.59

15 33 30 N 15 o 33' E 360.178 346.9803 96.6067 346.9911 96.5892D 5051.06 5358.18

284 35 40 N 75 o 25' W 305.123 76.8834 -295.2773 76.8925 -295.2921E 5127.95 5062.89

206 10 20 S 26 o 10' W 142.570 -127.9522 -62.8832 -127.9479 -62.8902 A 5000.00 5000.00

Error = -0.03681 0.05981 0.00000 0.00000Perimeter= 1233.01 Rel. Acc. = Area, ft 2 = 68148.1

Linear Misclosure = 0.07023 17,557 Area, ac. = 1.564127,995,984 128,132,280

136,296

Pt. Length, ft.

Surveying Traverse Computations

Azimuth Unadjusted Adjusted CoordinatesBearing

Spreadsheet created by Dr. Charles Patrick,Professor

Adjusted Coordinates


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Latitude Departure Northing Easting5000.00 5000.00-194.4647 258.6601

4805.54 5258.66-101.4710 2.9329

4704.06 5261.59346.9911 96.5892

5051.06 5358.18

76.8925 -295.29215127.95 5062.89

-127.9479 -62.89025000.00 5000.00

0.00000 0.00000 Area, ft 2 = 68148.1

Area, ac. = 1.564127,995,984 128,132,280

136,296

Adjusted Coordinates

eet created by Dr. Charles Patrick,Professor

A

B

C

D

E

A

Line

Pt.

410File 3 Area Coordinates Blackboard

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