## Divide a quadrilateral area into three equal portions

Moderator: andrew

mmasroorali
Junior Member
Posts: 16
Joined: Tue Feb 14, 2012 3:34 am

### Divide a quadrilateral area into three equal portions

Dear All,
I have a quadrilateral, not necessarily a rectangle or trapezium. I want to divide it into three equal portions with straight lines.

I understand that there are a number of combinations which will satisfy the above requirement. However, for me, the two lines will divide one side of the quadrilateral into three equal portions. I want to find out where to put the other ends of these two division lines on the opposite side of the quadrilateral.

For example, for the image at http://teacher.buet.ac.bd/mmasroorali/dividearea.png or http://www.bilder-upload.eu/show.php?fi ... 984448.png P and Q divide AD into three equal portions. Now, I want to find out points R and S on BC, so that the new three quadrilaterals have equal areas.

Last edited by mmasroorali on Thu Feb 23, 2012 9:01 am, edited 1 time in total.

Clive
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Location: UK

### Re: Divide a quadrilateral area into three equal portions

mmasroorali wrote:Dear All,
I have a quadrilateral, not necessarily a rectangle or trapezium. I want to divide it into three equal portions with straight lines.

I understand that there are a number of combinations which will satisfy the above requirement. However, for me, the two lines will divide one side of the quadrilateral into three equal portions. I want to find out where to put the other ends of these two division lines on the opposite side of the quadrilateral.

For example, for the image at http://www.bilder-upload.eu/show.php?fi ... 923709.png, P and Q divide AD into three equal portions. Now, I want to find out points R and S on BC, so that the new three quadrilaterals have equal areas.

If you have 2 parallel sides you can quite easily use the points on a line option. Just set the points to divide the lines into 4 equal points and draw straight lines between them, which will give you 3 equal areas.

If you have no parallel sides it needs a bit more geometry thinking to take place!

mmasroorali
Junior Member
Posts: 16
Joined: Tue Feb 14, 2012 3:34 am
As I have pointed out none of the sides are parallel or some such. The quadrilateral is totally irregular, if you know what I mean.

Can qcad help in any way rather than using plain simple geometry or trial and error?

Husky
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Posts: 2490
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Location: USA

### Re: Divide a quadrilateral area into three equal portions

@clive

Maybe this will work

mmasroorali
Junior Member
Posts: 16
Joined: Tue Feb 14, 2012 3:34 am
Perhaps comma after the link was not properly interpreted. Updated links in the first post.

Husky
Moderator/Drawing Help/Testing
Posts: 2490
Joined: Wed May 11, 2011 9:25 am
Location: USA
mmasroorali wrote: Can qcad help in any way rather than using plain simple geometry or trial and error?
I loved to see me mistaken but I assume that QCad can be only be a part of this solution. It is easy to divide A-D in three equal pieces and it also a piece in a cake to get from QCad the hole Polygonal Area which can be divided by 3 what will be the base for further calculation. But the rest is plain geometry.

mmasroorali
Junior Member
Posts: 16
Joined: Tue Feb 14, 2012 3:34 am
Thanks for your reply and hints. Once I get the whole polynomial area and divide it by three to the get individual area, it will mean putting this value in some form of equation to be solved.

I was wondering whether this can be avoided by some automatic feature of qcad. Looks like it can not be.

Any other ideas will be appreciated.

J-J
Moderator
Posts: 408
Joined: Tue Mar 24, 2009 9:48 pm

### Divide a quadrilateral area into three equal portions

A fairly simple way to do that can be achieved with the tool "polygonal area", although not 100% accurate.
first select "N points on a line"to localize the origin of your two dividing lines (N=4 in this case).
mark the two points with a crossing line so they are better seen.
Select "polygonal area to obtain the total value. calculate 1/3.
Now, with the same tool, start at the first dividing point, progress to nearest corner of polygon, then to next. After you obtain the triangle, select "snap to entity" and follow the third side of your polygon until the value of 1/3 area is obtained. By zooming in at that point, you will increase your accuracy.
When your value is satisfactory, right click the mouse to quit the tool without moving, the reference point will remain on your line at the defined position.
Select a line tool to mark it before repeating the process for the second section.
When finished draw your lines from point to point and erase unnecessary ones.
It is quicker to do than to explain!
good luck

mmasroorali
Junior Member
Posts: 16
Joined: Tue Feb 14, 2012 3:34 am
Your method looks very attractive and should have saved me from solving a system of trigonometric equations. However, it looks like I might be missing something here.

The only option I find for area is, "Area of Polygon" (button with picture of a polygon in red). When I follow your instructions, after the third point have been selected, as I proceed to select the fourth point, no probable area is shown dynamically. I see only the coordinates of the three points selected so far. Only after I have selected the fourth point, and pressed the right mouse button to close the process, the area is displayed.

What is it I might be missing?

I am using 2.0.5.0 Free 1 Community Edition of qcad in Ubuntu.

andrew