Final answer:
To find the area of the shaded region, subtract the area of the square from the area of the circle. The area of a circle is πr², and the area of the square is (2r)². Calculate the areas and subtract to find the area of the shaded region.
Step-by-step explanation:
To find the area of the shaded region, we need to subtract the area of the square from the area of the circle. The area of a circle is calculated using the formula A = πr², where π is approximately 3.14 and r is the radius of the circle.
Given that the radius is 1.2 m, we can calculate the area of the circle as A = 3.14 × (1.2 m)² = 4.5238934 m². Rounding to the nearest hundredth, the area of the circle is 4.52 m².
Next, we need to calculate the area of the square. Since the length of each side of the square is equal to the diameter of the circle (2r), the area of the square is A = (2r)² = (2 × 1.2 m)² = 2.88 m². Rounding to the nearest hundredth, the area of the square is 2.88 m².
Finally, we can find the area of the shaded region by subtracting the area of the square from the area of the circle: 4.52 m² - 2.88 m² = 1.64 m². Rounding to the nearest hundredth, the area of the shaded region is 1.64 m².