Final answer:
The area of the rectangle would change by 6 square meters.
Step-by-step explanation:
To find out how much the area would change, we need to calculate the areas of both the original rectangle and the modified rectangle. The area of the original rectangle is obtained by multiplying its length (14 m) by its width (12 m), which gives us an area of 168 square meters.
Next, we calculate the area of the modified rectangle. The modified width is (12 m - 3 m) = 9 m and the modified length is (14 m + 4 m) = 18 m. Multiplying these values together gives us an area of 162 square meters.
The change in area is then given by subtracting the area of the modified rectangle from the area of the original rectangle: 168 square meters - 162 square meters = 6 square meters. So, the area would change by 6 square meters.