Question

How many rectangles are present in the given figure?

• A. 8
• B. 9
• C. 10
• D. 12

Hint:

When counting rectangles in diagonal grids, note that all rectangles appear as tilted squares formed by intersections of two perpendicular families of parallel lines; count by size (large/medium/small) and then include any axis-aligned boundary squares.

Answer 1

The Correct Option is C

Step 1: Observe that every rectangle in the figure is a square (possibly tilted). There is one outer square (axis-aligned). Inside, the two families of diagonal lines (\(/\) and \(\backslash\)) form a lattice of tilted squares (diamonds).
Step 2: Count tilted squares:
\(1\) large central diamond.
\(4\) medium diamonds adjacent to the central one (top, right, bottom, left).
\(4\) small corner diamonds formed near the vertices of the outer square.
Step 3: Adding the axis-aligned outer square gives the total number of rectangles: \[ 1\ (\text{outer}) + 1\ (\text{central}) + 4\ (\text{medium}) + 4\ (\text{small}) = 10. \] Hence, the figure contains \(\boxed{10}\) rectangles.