PARTITION OF LAND
This task may be carried out by an engineer when sub-dividing land either for large building plots or for sale purposes.
To cut off a required area by a line through a given point:
With reference to Figure 11.7, it is required to find the length and bearing of the line GH which divides the area ABCDEFA into the given values.
(1) Calculate the total area ABCDEFA.
(2) Given point G, draw a line GH dividing the area approximately into the required portions.
(3) Draw a line from G to the station nearest to H, namely F.
(4) From coordinates of G and F, calculate the length and bearing of the line GF.
(5) Find the area of GDEFG and subtract this area from the required area to get the area of triangle GFH.
(6) Now area GFH = 0.5HF × FG sin θ, difference FG is known from (4) above, and θ is the difference of the known bearings FA and FG and thus length HF is calculated.
(7) As the bearing FH = bearing FA (known), then the coordinates of H may be calculated.
(8) From coordinates of G and H, the length and bearing of GH are computed.
Divide an area by a line through a given point
To cut off a required area by a line of given bearing:
With reference to Figure , it is required to fix line HJ of a given bearing, which divides the area ABCDEFGA into the required portions.
(1) From any station set off on the given bearing a trial line that cuts off approximately the required area, say AX.
(2) Compute the length and bearing of AD from the traverse coordinates.
(3) In triangle ADX, length and bearing AD are known, bearing AX is given and bearing DX = bearing DE; thus the three angles may be calculated and the area of the triangle found.
(4) From coordinates calculate the area ABCDA; thus total area ABCDXA is known.
Divide an area by a line with a given bearing