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 E] approximate area of the lake? [Hint: Use the Law of Cosines on the three triangles shown, and then find the sum of their areas] v=40 ft,w=35ft,x=35ft,y=75ft, z=15ft,F=10,G=110 (E The approximate area of the lake is D El (Round the final answer to two decimal places as needed. Round all intermediate values to four decimal places as needed.)