To determine which statement is true, we need to analyze the arrangement of the three square blocks and the regions formed.
Let’s denote:
- The area of each square block as \( A \).
- The three squares, which can be considered as having equal area \( A \).
From the arrangement:
- Regions X, Y, and Z are formed by the overlapping sections of these squares.
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Statement A: The sum of the areas of Region Y and Region Z is equal to the area of Region X.
This would imply that the combined area of the overlapping regions is equal to the non-overlapping region, which may or may not be true, depending on the specific arrangement and overlap of the squares. Typically, this kind of statement is false unless specific geometric conditions hold. -
Statement B: The sum of the areas of Region Z and Region X is equal to the area of Region Y.
Similar to Statement A, this statement would imply a specific relationship between overlapping and non-overlapping areas, which may or may not be true. -
Statement C: The sum of the areas of Region X and Region Y is greater than the area of Region Z.
This statement suggests that the combined area of the regions that are not highly overlapping is greater than the area where they overlap. This is generally true because overlapping regions often result in lesser combined area due to shared sections being counted twice. -
Statement D: The sum of the areas of Region X and Region Y is equal to the area of Region Z.
This would imply that the non-overlapping regions have area equal to the overlapping area, which is not typical in configurations of overlapping squares.
Given this analysis, Statement C is the most likely to be true.
Therefore, the correct answer is: C: The sum of the areas of Region X and Region Y is greater than the area of Region Z.