At 11:48 PM 11/10/2006, you wrote:

>Hi all
>Just to further clarify on the second of my too
>questions:
>
>I am not concerned with volume. I am trying to work
>out area. The area of a crossection (a number of
>crossections actually). And it seems to me also that
>the average diameter will not have a direct
>relationship to the area, surely? For example, a line
>may have its longest diameter at 20cm and its shortest
>diameter at 0cm. Although its average diameter is
>therefore 10cm, its area is 0. That's why I thought
>there may be a more accurate way of working it out.
>For example, wouldn't an elipse use a different
>formula for working out the area than a circle? What I
>am measuring is closer to an elipse. However it is
>more irregular. It may aid you if I give you the image
>of a lake. How would we work out the area of a lake,
>when our available data is a number of diameter
>measurements of the lake?
>By the way I figured if I actually used the diameters
>to plot out a map on graph paper, I could count the
>little squares to find the area!! However, as I have
>to do a large number of such calculations, that is not
>practical. I feel sure there must be a suitable
>formula.
>
>Thank you!
>Best wishes
>Justin

My previous answer was based on knowing the radii from some center.
However, knowing diameters is more difficult, since they may not all
meet at a common center.

There might be a way to use a tree as a "center", but instead of
using a common angle, you must measure the distance of each point of
the lake from the tree, and the distance between consecutive chosen
points on the lake. The area of the triangles (no longer isosceles)
require a different formula. Also, triangles formed from points on
the near side of the lake must be subtracted from the triangles from
the far side of the lake. Some triangles have no area at all.


Ben Saucer
e-mail: bsaucer1@...
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