Question

Sarah joined three squares at their vertices to create the figure shown in the diagram. She then covered each of the three squares with square centimeter tiles.

Based on the information, which statement is true?
Responses
A The number of tiles needed to cover both Region P and Region R is greater than the number of tiles needed to cover Region S.The number of tiles needed to cover both Region P and Region R is greater than the number of tiles needed to cover Region S.
B The number of tiles needed to cover Region R is the same as the number of tiles needed to cover both Region P and Region S.The number of tiles needed to cover Region R is the same as the number of tiles needed to cover both Region P and Region S .
C The number of tiles needed to cover Region S is greater than the number of tiles needed to cover both Region P and Region R.The number of tiles needed to cover Region S is greater than the number of tiles needed to cover both Region P and Region R .
D The number of tiles needed to cover Region S is the same as the number of tiles needed to cover both Region P and Region R.


A simple 2D diagram shows a three-dimensional figure composed of three rectangular regions, labeled P, R, and S. 


Region P is a square-shaped region positioned on top left. 


Region R is a square-shaped region positioned to the right of Region P, sharing a common edge.


Region S is a square-shaped region positioned below and to the left of Regions P and R, touching Region P and R at a corner.


A shaded triangular region is located where Regions P, R, and S meet inside the three dimensional figure.

Answer 1

To analyze which statement is true based on the arrangement of the regions P, R, and S, let's first understand how the three squares are positioned:

1. **Region P**: A square in the top left.
2. **Region R**: A square to the right of Region P, sharing a common edge.
3. **Region S**: A square positioned below and to the left of Regions P and R, touching both at corners.

From this layout, we can make some deductions:

- Regions P and R share a common edge, indicating that they are directly adjacent and will likely have related dimensions.
- Region S touches Regions P and R only at their corners, suggesting that it does not share any full edges with them.

The relationship among the regions:
- Since Regions P and R are adjacent, depending on their dimensions, they would together cover more area than Region S, which is positioned beneath them.

Let's consider the possible truths of the given statements:

**A:** "The number of tiles needed to cover both Region P and Region R is greater than the number of tiles needed to cover Region S."
- This statement seems plausible because Regions P and R share a side and will likely cover more area collectively than Region S, which only touches the corners.

**B:** "The number of tiles needed to cover Region R is the same as the number of tiles needed to cover both Region P and Region S."
- This statement is less likely true, as Region R and Region P together (considering their adjacent positions) would cover more area than just Region S.

**C:** "The number of tiles needed to cover Region S is greater than the number of tiles needed to cover both Region P and Region R."
- This is unlikely since we have already established that Regions P and R should cover more area than Region S.

**D:** "The number of tiles needed to cover Region S is the same as the number of tiles needed to cover both Region P and Region R."
- This statement is also unlikely because they are positioned differently, and thus their areas will not equate.

Based on this analysis, the most plausible true statement from the given options is:

**A:** The number of tiles needed to cover both Region P and Region R is greater than the number of tiles needed to cover Region S.