Chemical Science and Geometry: Composting and Areas

The composting method is to be used to remediate a contaminated site. Composting consists of the degradation of the contaminants to simpler, nontoxic compounds using organic material. The site has the following shape.

There is a small lake on one of the borders of the site, which has an area of 0.15 km2in common with the property. If one bag of compost can handle 3850 m2of land area, what is the minimum number of bags required to remediate this property (lake not included)?

Solution:

We need to find the area of the triangular site. We know the length of side AB, so lets find side BC and AC and use Hero's Formula for the area.

In triangle ABC, using the Law of Sines;

From Hero's Formula, the area of a triangle, A , is given by:

Here, s= (1.50 + 2.451 + 1.329)/2 = 2.64

And the # of bags required =

∴ A minimum of 186 bags of compost is required to remediate this site.

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Written by Arch McFarlane, June 2003