# How do I find the area of a polygon covered by points of a defined size? (QGIS 2.18)

I'm using point vectors to portray 264 marked trees in a stand using the 'Random points inside polygons' tool (it doesn't matter where they are). Each point is 4.5m across (the average single tree canopy).

How do I find the proportion of the area of the polygon covered by the points in order to work out the proportion of canopy to be removed? Either the area covered by red or the area covered by 264 4.5m points would do (as some trees are on the edge). • You're gonna need to clarify the question, because it's not clear yet. Try to start like this: 1) With the help of the Random Points Inside Polygons tool, I have created random dots in the form of red dots shown in the figure. 2) Then I created buffer zones with a diameter of 4.5 meters using the Buffer tool, etc. – Cyril Oct 12 '19 at 11:24
• What's unclear to me is what you're seeking you don't already have ... : you got the area covered by the trees (hand calculation ...) and if u're seeking the area of your polygon you can use for example the identify tool (blue "i" button) ... If you have the two data you can calculate the proportion i guess ? But if you want to handle the special case of the trees located on the edges it will be less obvious ... – snaileater Oct 12 '19 at 11:58

First of all, make sure your data is in a projected coordinate system whose linear unit is "Meter"

Approximate Solution:

In the tree stand polygon's attribute table, use Field Calculator to make a new field with the expression `\$area - (264 * (4.5/2)^2 * 3.14)`. Make sure the field type is "Real" or some other numeric type.

This however will not take into account trees which are on the edge

Exact Solution:

1. Use Vector > Geoprocessing Tools > Buffer to buffer the points by 2.25.

2. Use Vector > Geoprocessing Tools > Clip to clip the tree stand polygon with the buffered tree polyons

3. Use the field calculator in the resultant layer's attribute table to calculate the area of all the features by using the expression `\$area`

This will give you the exact amount of area from each tree's canopy, taking into account overlaps from nearby trees and trees near the edge of the stand