Elizabeth (from Exercise 9) is designing another backyard pond for her company. She follows the same procedure to find the area. She first creates an x by y rectangle to frame her pond design. She generates 10,000 random points inside the rectangle and p points land inside the pond. Express the area of the pond algebraically.

Data from Exercise 9

Elizabeth is a landscape designer. She designed a small pond with a fountain that her company plans to manufacture and market. It is a free-form shape, and the company wants to include the area of the pond on the packaging.

a. She takes a model of the pond and places it inside a 25-ft by 25-ft square. What is the area of the square?

b. She then takes a photo of the pond in the square. Then, using a graphing calculator, she generates 5,000 random points inside the square with the pond. She finds that 3,200 of these points land inside the pond outline. What percent of the points landed in the pond?

c. What is the area of the pond, to the nearest square foot?