To approximate the area of a​ lake, a surveyor walks around the perimeter of the​ lake, taking the measurements shown in the illustration with values below. Using this​ technique, what is the approximate area of the​ lake? [Hint: Use the Law of Cosines on the three triangles​ shown, and then find the sum of their​ areas.]
vequals40 ​ft, wequals40 ​ft, xequals30 ​ft, yequals85 ​ft, zequals25 ​ft, Fequals10degrees​, Gequals105degrees
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Part 1
x
y
z
v
w
G
F
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Part 1
The approximate area of the lake is

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ft.
ft squared .
ft cubed .