Question

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? (express your answer in square feet) 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?

Answer 1

a. The area of the square is 25 feet x 25 feet = 625 square feet.

b. To find the percent of points that landed in the pond, we divide the number of points that landed in the pond by the total number of points generated and multiply by 100.

3,200 points / 5,000 points = 0.64

0.64 x 100 = 64%

so 64% of the points landed in the pond.

c. To find the area of the pond, we multiply the proportion of points that landed in the pond by the area of the square.

64% of the points landed in the pond = 0.64

Area of the pond = 0.64 x 625 square feet = 400 square feet. So, the area of the pond, to the nearest square foot, is 400 square feet.

Explanation: