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 v 45 ft w 45 ft x 30 ft y 75 ft z 20 ft F 15 G 105 CRE The approximate area of the lake is Round the final answer to two decimal places as needed Round all intermediate values to four decimal places as needed W