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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

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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

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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

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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)

29
#xy
1526289.3936179080.799
2526288.2976179076.651
3526284.6426179060.426
4526284.5446179055.234
5526287.1526179052.352
6526320.8906179042.888
7526322.1276179042.682
8526347.5046179035.559
9526380.3226179036.556
10526385.9486179036.726
11526381.5196179075.715
12526382.1746179081.025
13526382.4906179084.201
14526383.2176179090.595
15526382.9336179091.600
16526381.9426179093.080
17526379.8176179094.087
18526375.1966179095.415
19526372.6126179096.157
20526364.7586179096.063
21526358.3706179097.196
22526356.8996179097.322
23526335.7496179100.980
24526325.6336179102.730
25526315.6836179104.935
26526302.6776179108.086
27526299.8536179107.679
28526298.1986179106.295
29526289.3936179080.799

The last corner is the same as the first, so the ring is closed.

Source: Datafordeler Matriklen via Grundfast · fetched

Questions 1 / 4

Correct so far: 0

What does the shoelace formula give for the land parcel's 28 corners?