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.

top best enrichment tuition centre primary mathematics

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.

top maths primary enrichment tuition centre

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


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.

best top mathematics enrichment tuition singapore

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.

Share with this puzzle with your friends & subscribe to our newsletter to receive your regular dose of earth-shattering educational tips!