Quick Calculation for Land Subdivision in GIS Settings

Question: Offset one edge of a quadrilateral (since get a new edge ) to form a new (usually smaller) quadrilateral (parcel) of which area equals to a predefined value . Find the offset distance .

Short answer: find the linear equation between offset distance and offset edge , then solve the quadratic equation of offset :

It’s easy to pick the right root as the solution for .

The linear relationship of and can be easily got from trigonometry:

The quadratic equation of is:

There is another ways to explain .

Let be the origin, , and are vectors, then , , where is the scale ratio.
Then the linear equation of and can be proved.

From the perspective of similar triangles,

Simplified as:

In a GIS work environment, offset a line or read length value of a line is straightforward and convenient. In order to get the equation of and , a trick can be used here.

Start from the general form:

Let , then

Offset by a specific value, say 10, read from GIS software, then

Problem solved without angles or distance of which could be far away.

My practice is putting the logic into a Excel form with 3 parameters.

Area of New Parcel in
Length of Original Edge in
Length of Edge by offset in
Required Offset in B69: =IFERROR((-B67+SQRT(B67B67+2(B68-B67)/10*B66))/((B68-B67)/10),0)