12 AREA
Asterisks indicate problems that have answers given in Appendix G.
*12.1 Compute the area enclosed within polygon ABDFGA of Figure 12.1 using triangles.
12.2 Similar to Problem 12.1, except for polygon BGDCB of Figure 12.1.
12.3 Compute the area enclosed between line AGBA and the shoreline of Figure 12.1 using
the offset method.
(*)
12.6 Repeat Problem 12.5 with the following offset in meters.
Offset Point
A
B
C
D
E
F
G
Stationing
0.000
20.000
78.940
148.963
163.654
203.691
250.454
Offset
2.15
3.51
4.04
6.57
5.87
4.64
1.65
1099 m2 or 0.1099 ha;
Computations
0
20
78.94
148.963
163.65
203.69
250.454
2.15
3.51
4.04
6.57
5.87
4.64
1.65
56.6
222.5
371.472
91.378
210.39
147.07
12.7 Use the coordinate method to compute the area enclosed by the traverse of Problem
10.8.
5000.00
1818.73
3839.67
2810.22
5248.32
9545277.034
1522.81
5531.30
15544169.89
531.47
6704.64
10209892.84
5000.00
37,956,689.8
630.890
1311.410
714652.9
544.950
1105.620
747786.1
12.9 Compute the area enclosed in the traverse of Problem 10.8 using DMDs.
21,081,518
483.965
Check by DMD
Dep
Lat
DMD
D-Area
7.7822
−2862.544
7.782
−22276.88992
4186.9438
−132.3871
4202.508
−556357.8733
2108.19
3179.7891
10497.642
33380287.61
−3288.1997
1573.6647
9317.632
14662829.04
−3014.7163
−1758.5227
3014.716
−5301447.048
42163034.83
21,081,517
483.965
12.13 Calculate the area inside the traverse of Problem 10.18 by coordinates and check by
DMDs.
54632861.41
57104932.16
51265244.4
212459555.8
213063580.2
Dep
D-Area
399.502
58.17
23239.03134
23756.97153
−631.559
−753611.5661
199.873
102592.2126
−604023.3507
12.14 Compute the area enclosed by the traverse of Problem 10.19 using the DMD method.
Check by coordinates.
*12.16 Determine the area of the lot in Problem 10.26.
12.22 Compute by DMDs the area in hectares within a closed-polygon traverse ABCDEFA by
placing the X and Y axes through the most southerly and most westerly stations,
respectively. Departures and latitudes (in meters) follow. AB: E dep. 30, N lat. = 40; BC:
E dep. = 70, N lat. = 10; CD = E dep. = 30, S lat = 50; DE: W dep = 60, S lat. = 40; EF:
W dep = 90, S lat = 30; FA: E dep. = 20, N lat = 70.
12.24 Calculate the area of a piece of property bounded by a traverse and circular arc with the
following coordinates in feet at angle points: A (445.18, 913.88), B (453.67, 835.51), C
(663.67, 835.51), D (663.67, 935.51), E (465.12, 936.04) with a circular arc of radius
19.99 ft starting at E, tangent to DE, and ending at A.
12.26 Partition the lot of Problem 12.24 into two
equal areas by means of a line parallel to BC.
Tabulate in clockwise consecutive order the
lengths and azimuths of all sides of each
12.27 Lot ABCD between two parallel street lines is 350.00 ft
deep and has a 220.00 ft frontage (AB) on one street and
a 260.00 ft frontage (CD) on the other. Interior angles
at A and B are equal, as are those at C and D. What
distances AE and BF should be laid off by a surveyor to
divide the lot into two equal areas by means of a line EF
12.28 Partition 1-acre parcel from the northern part of
lot ABCDEFA in Problem 12.21 such that its
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