Problem No. 318

area cdef = 18232.0373
area bcfg = 15483.6146
area abcfg = 51699.9

Too easy in CAD.

In the County I survey we have to wait for County assessor‰Ûªs office to map it before we know who gets what. 🙂 Then we can calc the area. I say this in jest but there seems to be a lot of truth in what I say. My 2 cents, Jp

GROSS AREA INCLUDING HIGH WAY AND SIDE STREET:
Points entered clockwise.
Calculating...
J N22å¡57'04"E dist= 368.150 N= 10665.125 E= 14660.991 C'
C' S67å¡02'56"E dist= 66.000 N= 10639.389 E= 14721.766 C
C S23å¡31'00"E dist= 510.843 N= 10170.974 E= 14925.600 F
F S34å¡03'03"W dist= 100.000 N= 10088.120 E= 14869.607 F'
F' N55å¡56'57"W dist= 425.053 N= 10326.119 E= 14517.433 J
Results:
Square Feet : 113185.5 Acres : 2.598
NET AREA TO C/L OF VACATED R/W:
Points entered clockwise.
Calculating...
A N22å¡57'04"E dist= 233.674 N= 10597.474 E= 14704.017 B
B N22å¡57'04"E dist= 45.518 N= 10639.389 E= 14721.766 C
C S23å¡31'00"E dist= 510.843 N= 10170.974 E= 14925.600 F
F N55å¡56'57"W dist= 61.532 N= 10205.427 E= 14874.618 G
G N55å¡56'57"W dist= 315.882 N= 10382.298 E= 14612.897 A
Results:
Square Feet : 51699.9 Acres : 1.187
AREA VACATED R/W SOUTHWESTERLY OF C/L:
Points entered clockwise.
Calculating...
B N22å¡57'04"E dist= 45.518 N= 10639.389 E= 14721.766 C
C S23å¡31'00"E dist= 510.843 N= 10170.974 E= 14925.600 F
F N55å¡56'57"W dist= 61.532 N= 10205.427 E= 14874.618 G
G N23å¡31'00"W dist= 427.558 N= 10597.474 E= 14704.017 B
Results:
Square Feet : 15483.6 Acres : 0.355
AREA VACATED R/W NORTHEASTERLY OF C/L:
Points entered clockwise.
Calculating...
C N22å¡57'04"E dist= 45.518 N= 10681.304 E= 14739.516 D
D S23å¡31'00"E dist= 594.129 N= 10136.520 E= 14976.582 E
E N55å¡56'57"W dist= 61.532 N= 10170.974 E= 14925.600 F
F N23å¡31'00"W dist= 510.843 N= 10639.389 E= 14721.766 C
Results:
Square Feet : 18232.0 Acres : 0.419

GROSS AREA INCLUDING HIGH WAY AND SIDE STREET:
Points entered clockwise.
Calculating...
J N22å¡57'04"E dist= 368.150 N= 10665.125 E= 14660.991 C'
C' S67å¡02'56"E dist= 66.000 N= 10639.389 E= 14721.766 C
C S23å¡31'00"E dist= 510.843 N= 10170.974 E= 14925.600 F
F S34å¡03'03"W dist= 100.000 N= 10088.120 E= 14869.607 F'
F' N55å¡56'57"W dist= 425.053 N= 10326.119 E= 14517.433 J
Results:
Square Feet : 113185.5 Acres : 2.598
NET AREA TO C/L OF VACATED R/W:
Points entered clockwise.
Calculating...
A N22å¡57'04"E dist= 233.674 N= 10597.474 E= 14704.017 B
B N22å¡57'04"E dist= 45.518 N= 10639.389 E= 14721.766 C
C S23å¡31'00"E dist= 510.843 N= 10170.974 E= 14925.600 F
F N55å¡56'57"W dist= 61.532 N= 10205.427 E= 14874.618 G
G N55å¡56'57"W dist= 315.882 N= 10382.298 E= 14612.897 A
Results:
Square Feet : 51699.9 Acres : 1.187
AREA VACATED R/W SOUTHWESTERLY OF C/L:
Points entered clockwise.
Calculating...
B N22å¡57'04"E dist= 45.518 N= 10639.389 E= 14721.766 C
C S23å¡31'00"E dist= 510.843 N= 10170.974 E= 14925.600 F
F N55å¡56'57"W dist= 61.532 N= 10205.427 E= 14874.618 G
G N23å¡31'00"W dist= 427.558 N= 10597.474 E= 14704.017 B
Results:
Square Feet : 15483.6 Acres : 0.355
AREA VACATED R/W NORTHEASTERLY OF C/L:
Points entered clockwise.
Calculating...
C N22å¡57'04"E dist= 45.518 N= 10681.304 E= 14739.516 D
D S23å¡31'00"E dist= 594.129 N= 10136.520 E= 14976.582 E
E N55å¡56'57"W dist= 61.532 N= 10170.974 E= 14925.600 F
F N23å¡31'00"W dist= 510.843 N= 10639.389 E= 14721.766 C
Results:
Square Feet : 18232.0 Acres : 0.419

[pre]
GROSS AREA INCLUDING HIGH WAY AND SIDE STREET:
Points entered clockwise.
Calculating...
J N22å¡57'04"E dist= 368.150 N= 10665.125 E= 14660.991 C'
C' S67å¡02'56"E dist= 66.000 N= 10639.389 E= 14721.766 C
C S23å¡31'00"E dist= 510.843 N= 10170.974 E= 14925.600 F
F S34å¡03'03"W dist= 100.000 N= 10088.120 E= 14869.607 F'
F' N55å¡56'57"W dist= 425.053 N= 10326.119 E= 14517.433 J
Results:
Square Feet : 113185.5 Acres : 2.598

NET AREA TO C/L OF VACATED R/W:
Points entered clockwise.
Calculating...
A N22å¡57'04"E dist= 233.674 N= 10597.474 E= 14704.017 B
B N22å¡57'04"E dist= 45.518 N= 10639.389 E= 14721.766 C
C S23å¡31'00"E dist= 510.843 N= 10170.974 E= 14925.600 F
F N55å¡56'57"W dist= 61.532 N= 10205.427 E= 14874.618 G
G N55å¡56'57"W dist= 315.882 N= 10382.298 E= 14612.897 A
Results:
Square Feet : 51699.9 Acres : 1.187

AREA VACATED R/W SOUTHWESTERLY OF C/L:
Points entered clockwise.
Calculating...
B N22å¡57'04"E dist= 45.518 N= 10639.389 E= 14721.766 C
C S23å¡31'00"E dist= 510.843 N= 10170.974 E= 14925.600 F
F N55å¡56'57"W dist= 61.532 N= 10205.427 E= 14874.618 G
G N23å¡31'00"W dist= 427.558 N= 10597.474 E= 14704.017 B
Results:
Square Feet : 15483.6 Acres : 0.355

AREA VACATED R/W NORTHEASTERLY OF C/L:
Points entered clockwise.
Calculating...
C N22å¡57'04"E dist= 45.518 N= 10681.304 E= 14739.516 D
D S23å¡31'00"E dist= 594.129 N= 10136.520 E= 14976.582 E
E N55å¡56'57"W dist= 61.532 N= 10170.974 E= 14925.600 F
F N23å¡31'00"W dist= 510.843 N= 10639.389 E= 14721.766 C
Results:
Square Feet : 18232.0 Acres : 0.419
[/pre]

<pre>
GROSS AREA INCLUDING HIGH WAY AND SIDE STREET:
Points entered clockwise.
Calculating...
J N22å¡57'04"E dist= 368.150 N= 10665.125 E= 14660.991 C'
C' S67å¡02'56"E dist= 66.000 N= 10639.389 E= 14721.766 C
C S23å¡31'00"E dist= 510.843 N= 10170.974 E= 14925.600 F
F S34å¡03'03"W dist= 100.000 N= 10088.120 E= 14869.607 F'
F' N55å¡56'57"W dist= 425.053 N= 10326.119 E= 14517.433 J
Results:
Square Feet : 113185.5 Acres : 2.598
NET AREA TO C/L OF VACATED R/W:
Points entered clockwise.
Calculating...
A N22å¡57'04"E dist= 233.674 N= 10597.474 E= 14704.017 B
B N22å¡57'04"E dist= 45.518 N= 10639.389 E= 14721.766 C
C S23å¡31'00"E dist= 510.843 N= 10170.974 E= 14925.600 F
F N55å¡56'57"W dist= 61.532 N= 10205.427 E= 14874.618 G
G N55å¡56'57"W dist= 315.882 N= 10382.298 E= 14612.897 A
Results:
Square Feet : 51699.9 Acres : 1.187
AREA VACATED R/W SOUTHWESTERLY OF C/L:
Points entered clockwise.
Calculating...
B N22å¡57'04"E dist= 45.518 N= 10639.389 E= 14721.766 C
C S23å¡31'00"E dist= 510.843 N= 10170.974 E= 14925.600 F
F N55å¡56'57"W dist= 61.532 N= 10205.427 E= 14874.618 G
G N23å¡31'00"W dist= 427.558 N= 10597.474 E= 14704.017 B
Results:
Square Feet : 15483.6 Acres : 0.355
AREA VACATED R/W NORTHEASTERLY OF C/L:
Points entered clockwise.
Calculating...
C N22å¡57'04"E dist= 45.518 N= 10681.304 E= 14739.516 D
D S23å¡31'00"E dist= 594.129 N= 10136.520 E= 14976.582 E
E N55å¡56'57"W dist= 61.532 N= 10170.974 E= 14925.600 F
F N23å¡31'00"W dist= 510.843 N= 10639.389 E= 14721.766 C
Results:
Square Feet : 18232.0 Acres : 0.419
</pre>

The gross area of the triangular parcel should include the portion under High Way and Side Street which I calculated by running out perpendicular to the centerline from F and C.

GROSS AREA INCLUDING HIGH WAY AND SIDE STREET:
Points entered clockwise.
Calculating...
J N22å¡57'04"E dist= 368.150 N= 10665.125 E= 14660.991 C'
C' S67å¡02'56"E dist= 66.000 N= 10639.389 E= 14721.766 C
C S23å¡31'00"E dist= 510.843 N= 10170.974 E= 14925.600 F
F S34å¡03'03"W dist= 100.000 N= 10088.120 E= 14869.607 F'
F' N55å¡56'57"W dist= 425.053 N= 10326.119 E= 14517.433 J
Results:
Square Feet : 113185.5 Acres : 2.598
NET AREA TO C/L OF VACATED R/W:
Points entered clockwise.
Calculating...
A N22å¡57'04"E dist= 233.674 N= 10597.474 E= 14704.017 B
B N22å¡57'04"E dist= 45.518 N= 10639.389 E= 14721.766 C
C S23å¡31'00"E dist= 510.843 N= 10170.974 E= 14925.600 F
F N55å¡56'57"W dist= 61.532 N= 10205.427 E= 14874.618 G
G N55å¡56'57"W dist= 315.882 N= 10382.298 E= 14612.897 A
Results:
Square Feet : 51699.9 Acres : 1.187
AREA VACATED R/W SOUTHWESTERLY OF C/L:
Points entered clockwise.
Calculating...
B N22å¡57'04"E dist= 45.518 N= 10639.389 E= 14721.766 C
C S23å¡31'00"E dist= 510.843 N= 10170.974 E= 14925.600 F
F N55å¡56'57"W dist= 61.532 N= 10205.427 E= 14874.618 G
G N23å¡31'00"W dist= 427.558 N= 10597.474 E= 14704.017 B
Results:
Square Feet : 15483.6 Acres : 0.355
AREA VACATED R/W NORTHEASTERLY OF C/L:
Points entered clockwise.
Calculating...
C N22å¡57'04"E dist= 45.518 N= 10681.304 E= 14739.516 D
D S23å¡31'00"E dist= 594.129 N= 10136.520 E= 14976.582 E
E N55å¡56'57"W dist= 61.532 N= 10170.974 E= 14925.600 F
F N23å¡31'00"W dist= 510.843 N= 10639.389 E= 14721.766 C
Results:
Square Feet : 18232.0 Acres : 0.419

What is cool about this problem is it can all be done with judicious use of the Pythagorean Theorem and Trigonometry. No COGO or CAD is required.

vern, post: 328444, member: 3436 wrote: area cdef = 18232.0373
area bcfg = 15483.6146
area abcfg = 51699.9

Too easy in CAD.

.0373? ... really? 🙂 (almost forgot the smiley face)

Tom Adams, post: 328708, member: 7285 wrote: .0373? ... really? 🙂 (almost forgot the smiley face)

Dagnabit the zoning minimum is 18232.0374, missed it by that --><-- much 😉

Well, here we are 6 pages deep now so here's my answer (everyone else was right).

My first attempt at using COGO (Microsurvey), I established a coordinate at H, then traversed to J. Then a COGO'd my way to A. I resorted to CAD at that point drawing a circle of radius 202.41 then drawing a line from H to a tangent snap to Dave's solution point L then finished the rest with COGO.

Then I did it by hand but I didn't use any coordinates, I just broke it down into triangle. I did triangle H-A-L-H using the Pythagorean Theorem but could've used the Tangent-1 of 202.41 over distance H to A to get the angle A-H-L. I carried it to four places in distance and nearest second in angles. Later I did it again to five places and nearest 1/10th second which matched my COGO better.

Then I figured out you can establish H, J, and A in COGO. Then do a distance-distance intersection from A and H, the distance northeasterly from A is 2 times 202.41', the distance northwesterly from H is the distance from H to A. Call this point L2. Establish point L on-line to point L2 at 202.41' northeasterly from point A then the rest is basic COGO work.