Question

The owners of an amusement park want to add more rides and an arcade 2 in an open field. Below is a sketch of their plan. The owners do not know all of the measurements of the field. Using Distributive Property: Write TWO ways the owners could find the area of the whole field. a) By multiplying the length and width of the field separately

b) By dividing the field into smaller rectangles and adding their areas
c) By using the Pythagorean theorem
d) By estimating the area based on the sketch

Answer 1

The amusement park owners can find the field's area by multiplying the length by width for a simple rectangle or by dividing the field into smaller rectangles, calculating each area, and adding them together.

Step-by-step explanation:

To find the area of the whole field, the owners of an amusement park can use two methods using the Distributive Property:

1. By dividing the field into smaller rectangles, calculating the area of each, and then adding them together.
2. By multiplying the length by the width if the entire field is a single rectangle.

For example, if they have a field that is 20 meters by 30 meters, they can calculate the area by multiplying these two dimensions (20m * 30m = 600m²). If the area is not a perfect rectangle and consists of different sections, they should calculate the area of each section separately and then add them up. They can also use proportions and mental math to estimate areas when comparing two similar spaces. Proportions and unit understanding are essential in these calculations.

Remembering that the unit for area is always in square units will help prevent confusion between linear measurements and areas. Understanding the proportions and the use of units are crucial to correctly figuring out areas, especially when dealing with complex shapes or when making estimations.