[Figure: ABCD is a square; E, F, G, H are the mid-points of sides AB, BC, CD, DA respectively. Lines EG and HF divide the square into four equal smaller squares. Each smaller square is further divided into two equal rectangles: the top-left and bottom-right smaller squares by a horizontal line, and the top-right and bottom-left smaller squares by a vertical line.]
What is the number of rectangles which are NOT squares in the above figure? (Given that ABCD is a square and E, F, G, H are mid-points of its sides)
- A14
- B16
- C20
- D21
Explanation
Counting all axis-aligned rectangles formed by the grid lines in the figure gives 21 rectangles in total (verified by enumeration). Five of these are squares – the four quarter-squares and ABCD itself – leaving 21 − 5 = 16 non-square rectangles. Hence (B).