Final answer:
To find the area of the shaded sector, calculate the area of the entire circle and then multiply it by the fraction of the central angle. The area of the circle is approximately 4.5 m², and the area of the shaded sector is approximately 0.9252 m².
Step-by-step explanation:
To find the area of the shaded sector, we first need to find the area of the entire circle. The formula for the area of a circle is A = πr², where r is the radius. In this case, the radius is given as 12 m, so the area of the circle is A = 3.1415927...(12 m)² = 452.38934 m². However, since the radius has only two significant figures, the calculated quantity is limited to two significant figures, so the area of the circle is approximately 4.5 m².
The shaded sector has a central angle of 74 degrees. The formula for the area of a sector is A = (θ/360°) * A_c, where θ is the central angle and A_c is the area of the circle. Plugging in the values, we get A = (74°/360°) * 4.5 m² = 0.2056 * 4.5 m² = 0.9252 m². Therefore, the area of the shaded sector is approximately 0.9252 m².