To determine which statement is true regarding the areas of the shapes involved (ABCD, DGA, DEFG, GHIA), we would typically need to analyze the relationships between these areas based on a diagram. Since I cannot see the diagram, I can only help you reason through the possibilities based on common area relationships in geometry.
Consider the following guideline for the statements provided:
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A: This is saying that the area of shape ABCD minus the area of DGA is equal to the area of DEFG, which could imply that DGA is a part of ABCD and DEFG is the remaining section. If that holds true, this could be a valid statement.
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B: This means the area of ABCD minus the area of GHIA is equal to the area of DGA. This could suggest GHIA is outside of ABCD in a way that frames DGA which does not seem likely.
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C: This suggests that the sum of areas ABCD and DGA equals the area of GHIA. This situation needs specific conditions to be true and is less likely.
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D: This statement indicates that the sum of areas of ABCD and GHIA equals the area of DEFG. This may also suggest a spatial relationship depending on how these shapes are laid out.
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E: This says the sum of areas DEFG and GHIA is equal to the area of ABCD. This could make sense if DEFG and GHIA together completely fill ABCD.
Without the specific relationships shown in the diagram, it's hard to determine exactly which statement is true. However, if you can provide more detail about the arrangement of the shapes, then we can logically deduce which statement holds true!
If you can check the diagram and see how the areas relate (for instance, if one area is indeed a subtraction or addition of the others), you can confirm or deny each statement based on those relationships.