Final answer:
The area of the larger polygon is 3600 ft².
Step-by-step explanation:
The sides of two similar polygons are in the ratio of 5:2. To find the area of the larger polygon, we need to find the scale factor between the sides and use it to determine the scale factor between the areas. The scale factor between the sides is 5:2, which means the larger polygon is scaled up by a factor of 5/2. Since area is a two-dimensional measurement, the scale factor for area is the square of the scale factor for sides. Therefore, the area of the larger polygon would be (5/2)^2 = 25/4 times the area of the smaller polygon.
Given that the area of the smaller polygon is 576 ft², the area of the larger polygon can be calculated as follows:
Area of larger polygon = (25/4) * 576 ft²
Area of larger polygon = (25 * 576) / 4 ft²
Area of larger polygon = 14400 ft² / 4
Area of larger polygon = 3600 ft²
Therefore, the area of the larger polygon is 3600 ft².