Final answer:
To calculate the area of a regular polygon, specific formulas are used based on the polygon's characteristics. For a circle with radius r, having two significant figures, the area is calculated as A = πr² and then rounded to maintain the same level of precision, resulting in A = 4.5 m².
Step-by-step explanation:
To calculate the area of a regular polygon, you can apply various formulas depending on the information provided about the polygon, such as the length of the sides, the apothem, or the number of sides. However, the data provided refers to the calculation of the area of a circle based on the radius, which is a circular shape and not a polygon. The formula for the area (A) of a circle is A = πr², where π (pi) is approximately 3.1415927 and r is the radius. When calculating the area with a given radius that has two significant figures, such as r = 1.2 m, we must ensure that the final answer is also reported with two significant figures to maintain the correct level of precision.
Using a calculator with high precision and then rounding off to two significant figures, we get: A = π(1.2 m)² = 4.5238934 m². However, since the radius has only two significant figures, the area is correctly reported as A = 4.5 m².
In terms of a practical example, when estimating the area of a regulation basketball court using mental math, we can approximate based on known or estimated measurements. Instead of exact figures, we'd use rounded numbers to quickly calculate a rough area, focusing on the key message rather than full precision.