Measure the plot
A land parcel is a polygon. With the corners' coordinates you can calculate area and perimeter yourself — and compare with the register.
3 chapters · 4 questions
A land parcel in Jelling
Parcel no. 92 in the cadastral district “Jelling By, Jelling” lies in the middle of the Jelling monuments. The polygon has 28 corners in metres (coordinate system EPSG:25832). The corners are in the table below.
Source: Datafordeler Matriklen via Grundfast · fetched
The shoelace formula
The area of a polygon is half the sum of x(i)·y(i+1) − x(i+1)·y(i) all the way round. The perimeter is the sum of the distances between neighbouring corners. Put the corners in a spreadsheet and work it out yourself.
The answer and the surprise
Calculated from the corners, the area is 5,636.43 m² and the perimeter 301.11 m. The cadastre registers 5,531 m². The difference is 105.43 m², about 1.9%. The registered area is the plot's official figure; the calculated one shows that the polygon and the registered figure are not the same measurement.
Source: Datafordeler Matriklen via Grundfast · fetched
The land parcel's corners (metres, EPSG:25832)
| # | x | y |
|---|---|---|
| 1 | 526289.393 | 6179080.799 |
| 2 | 526288.297 | 6179076.651 |
| 3 | 526284.642 | 6179060.426 |
| 4 | 526284.544 | 6179055.234 |
| 5 | 526287.152 | 6179052.352 |
| 6 | 526320.890 | 6179042.888 |
| 7 | 526322.127 | 6179042.682 |
| 8 | 526347.504 | 6179035.559 |
| 9 | 526380.322 | 6179036.556 |
| 10 | 526385.948 | 6179036.726 |
| 11 | 526381.519 | 6179075.715 |
| 12 | 526382.174 | 6179081.025 |
| 13 | 526382.490 | 6179084.201 |
| 14 | 526383.217 | 6179090.595 |
| 15 | 526382.933 | 6179091.600 |
| 16 | 526381.942 | 6179093.080 |
| 17 | 526379.817 | 6179094.087 |
| 18 | 526375.196 | 6179095.415 |
| 19 | 526372.612 | 6179096.157 |
| 20 | 526364.758 | 6179096.063 |
| 21 | 526358.370 | 6179097.196 |
| 22 | 526356.899 | 6179097.322 |
| 23 | 526335.749 | 6179100.980 |
| 24 | 526325.633 | 6179102.730 |
| 25 | 526315.683 | 6179104.935 |
| 26 | 526302.677 | 6179108.086 |
| 27 | 526299.853 | 6179107.679 |
| 28 | 526298.198 | 6179106.295 |
| 29 | 526289.393 | 6179080.799 |
The last corner is the same as the first, so the ring is closed.
Source: Datafordeler Matriklen via Grundfast · fetched
Questions 1 / 4
What does the shoelace formula give for the land parcel's 28 corners?