



 
Hi Sarah, I reproduced your diagram and added some lines and labels.
You want to find the area of the region you shaded gray in your diagram. I will show you how to find half the area and then you can double it. I am going to find the area of EDB as the area of the sector BCD minus the area of the triangle BCE. The length of BE is 230.75/2 = 115.375 ft and the length of CE is 119.32  87 = 32.32 ft. Hence you can find the area of the triangle BCE using the fact that the area of a triangle is half the base times the height. All that remains is to find the area of the sector BCD. To determine this area I need the measure of the angle BCD. Tan(∠BCD) = BE/CE = 115.375/ 32.32 = 3.5698 and hence
The sector BCD is a fraction of the entire circle (π r^{2}) and the angle BCD is a fraction of 360^{o}. By the symmetry these fractions are the same, that is
Solve for the area of the sector BCD. Penny  


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