To find the area of the shaded region, we need to subtract the area of the square from the area of the circle:
Area of shaded region = Area of circle - Area of square
Area of shaded region = 81.3 - 16.1
Area of shaded region = 65.2 cm^2
The error interval for the area, a, of the shaded region can be found by considering the errors in the measurements of the areas of the circle and the square. For the area of the circle, the value is rounded to 1 decimal place, so the error is at most 0.05 cm^2 (half of the value of the smallest decimal place). For the area of the square, the value is truncated to 1 decimal place, so the error is at most 0.1 cm^2 (the value of the smallest decimal place).
Thus, the error interval for the area, a, of the shaded region is:
m < a < n
where:
m = 81.3 - 16.1 - 0.1 = 65.1 cm^2
n = 81.3 - 16.1 + 0.05 = 65.25 cm^2
Therefore, the error interval for the area, a, of the shaded region is:
65.1 < a < 65.25