Test Yourself: Which Area Is Bigger?


Diagram 1 shows two identical overlapping squares. A vertex of the red square is positioned exactly in the middle of the blue square. The smaller yellow square represents the overlapping area.

Diagram 1

In Diagram 2, the red square has been rotated about the vertex pinned to the middle of the blue square by 45⁰. The green triangle represents the new overlapping area.

Diagram 2

Question: How does the area of the yellow square compare with the area of the green triangle? (a) The yellow square has a smaller area than the green triangle

(b) The yellow square has a larger area than the green triangle

(c) The yellow square has the same area as the green triangle

Solution:

From Diagram 3, you can see that the yellow hatched triangle that is no longer part of the overlapping area is now replaced by a hatched green triangle of the same size in the new overlapping area.

Thus, the answer is (c)! In fact, the size of the overlapping area will always be constant (one quarter of the square) as the red square is rotated about that particular vertex.

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