Discussion
How many rectangles are present in the given figure?
Answer: C
The figure contains 10 rectangles.
The outer square is one. Inside it, the two diagonals and the four lines joining the midpoints of adjacent sides make two families of three parallel lines, one family at +45° and one at -45°, every line of one family crossing every line of the other at right angles. Any two lines from one family together with any two from the other enclose a rectangle (here, a square tilted at 45°), and all their corners lie on drawn segments:
\[ \binom{3}{2} \times \binom{3}{2} = 3 \times 3 = 9 \]
These are the four small tilted squares, the large central diamond, and four tilted rectangles each made of two adjacent small squares. With the outer square the total is 9 + 1 = 10. Forgetting the outer square gives 9, and 8 or 12 come from missing or double-counting some of the tilted rectangles.
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