Calculating Area of Land using simple levelling tools

Calculating Area of Land plot of un-equal sides just by using simple levelling tools Such as Auto level, Dumpy level etc.

Generally what we civil engineers are asked to build looks like the plan shown below (sometimes typical type plans for certain organizations), but actual land available may not suit it. Hence boundaries and area calculation becomes important. It is also important because your Plot Area should match the area mentioned in 7/12 so that future conflicts can be avoided.

Plot Area Calculator (Stadia + Bearing Method)

Number of Points:

Expected Building Plan (Just for Example)

Available Plot

Advantages:

1) Survey can be carried out using simple tools

2) Calculations are relatively easy (No complex trigonometry)

Concepts Used:

1) (Upper stadia reading - Lower stadia reading) × 100 = L

Where L → Distance between station and point where level is taken.

2) Lcosθ = Latitude (X-coordinate)    Lsinθ = Departure (Y-coordinate)

Where θ → Whole Circle Bearing (WCB)

3) Double Meridian Distance Method – To Calculate Area

Step 1:

Calculate Latitude (X-coordinate) & Departures (Y-coordinate) of all points

Point	Angle	Upper	Lower	Distance	Latitude (Xi)	Departure (Yi)	Distance between 2 points
1	329	1.37	0.855	51.5	44.1441159861588	-26.5244608578678	104.047
2	122	2.61	2.055	55.5	-29.4105191649429	47.0666693366816	135.446
3	234	5.201	4.156	104.5	-61.4235588645635	-84.542275912182	43.102
4	257	5.256	4.156	110	-24.7446159778252	-107.180707126376	106.071
5	329	1.37	0.855	51.5	44.1441159861588	-26.5244608578678

Step 2:

Use Double Meridian Distance Method to calculate area

SR	Xi	Yi	xi*yi+1	xi+1*yi	Difference
1	44.1441159861588	-26.5244608578678	2077.7165	780.0981	1297.6183
2	-29.4105191649429	47.0666693366816	2486.4322	-2891.0023	5377.4345
3	-61.4235588645635	-84.542275912182	6583.4204	2091.9661	4491.4543
4	-24.7446159778252	-107.180707126376	656.3376	-4731.3975	5387.7351
5	44.1441159861588	-26.5244608578678	0	0	0
Total					16554.2423

Area = ∑ (xi*yi+1 - xi+1*yi) / 2

Hence Area of polygon = 8277.121 sq.m

In 7/12 area is 8000 sq.m, hence it is necessary to consult Bhumiabhilekh department regarding boundaries and then plan accordingly.