On a map, 1 inch represents 5 miles. If a certain state is represented on a map by a rectangle 10 inches by 7.2 inches, what is the area of the state in square miles? A) \( 360 \mathrm{mi}^{2} \) B) \( 720 \mathrm{mi}^{2} \) C) \( 1,080 \mathrm{mi}^{2} \) D) \( 1,800 \mathrm{mi}^{2} \)

To find the area of the state represented on the map, you first calculate the area of the rectangle in inches. The area is 10 inches multiplied by 7.2 inches, which equals 72 square inches. Since 1 inch on the map represents 5 miles in reality, you need to convert square inches to square miles. Thus, you multiply the area in square inches by the conversion factor squared (5 miles/inch)^2. So, \(72 \, \text{square inches} \times (5 \, \text{miles/inch})^2 = 72 \times 25 = 1,800 \, \text{square miles}\). The correct answer is D) \( 1,800 \, \text{mi}^{2} \). Now, let's delve into some fun facts! Did you know that scale maps have been around since ancient times? The earliest known maps date back to Babylon around 600 BCE and were used for navigation and territorial claims. They were rudimentary but laid the groundwork for the advanced mapping techniques we have today, transforming the way we understand geography! For modern applications, consider how this knowledge aids in strategic planning for urban development or conservation efforts. Understanding land area from maps can guide decisions in resource allocation and help assess environmental impacts, showcasing how math and geography work hand-in-hand in real-world situations!