Please address questions 40, 41 and 42 below showing full workout

40. Computing the figure. Find the area of the shaded region enclosed in a semicircle of diameter 10 inches. The length of the chord PQ is 8 inches. [Hint: Triangle POR is a right triangle.] Q P 10 R 41. Cametry See the figure, which shows a circle of radius r with center at O. Find the area K of the shaded region as a function of the central angle 0. 42. Approximationg the Area of a Lake To approximate the area of a lake, a surveyor walks around the perimeter of the lake, taking the measurements shown in the illustration. 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.] 15 80 ft 35 ft 20 ft 40 ft 100 45 ft