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In order to improve the living environment of citizens, our city has built a leisure cultural square in a riverside space as shown in the figure, and built a rectangular pool in it, so that the fixed points are on the hypotenuse and the right angle respectively.

, open; They also form semicircles with diameters of, and respectively. They handed over two crescent moons (shaded in the picture) with flowers and plants on them; The rest of the open space is paved with tiles, including meters, meters and meters.

Resolution function between seeking and seeking;

When the value is taken, the area of the rectangle is the largest? What is the maximum area?

Find the area of two crescent moons (the shaded part in the figure), what is the value, and the sum of the areas of rectangles is equal to the area of two crescent moons?

This topic investigates the application of quadratic function in real life, involving the properties of rectangle, the solution of right triangle, trigonometric function, Pythagorean theorem, the properties of quadratic function, the area of triangle and so on. , comprehensive and difficult. The key to solving the problem is to use the idea of combining numbers with shapes and equations.