The figure below is made up of 9 identical squares. What fraction of the figure is not shaded?

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Worked solution

3

1. Determine the total area of the figure in terms of small squares.

The figure is a 3×33 \times 3 grid, so the total area is 99 squares.

2. Calculate the unshaded area in the top and middle rows.

Top row: The top-left and top-middle squares each have half unshaded (0.5+0.5=10.5 + 0.5 = 1 square). The top-right square is completely unshaded (11 square). Total for top row = 22 squares.
Middle row: The middle-left square has half unshaded (0.50.5 square). The middle-middle square is completely unshaded (11 square). The middle-right square is completely shaded (00 squares). Total for middle row = 1.51.5 squares.

3. Calculate the unshaded area in the bottom row.

Bottom row: The unshaded triangle across the bottom-left and bottom-middle squares has a base of 22 squares and a height of 11 square. Its area is 12×2×1=1\frac{1}{2} \times 2 \times 1 = 1 square. The bottom-right square has half unshaded (0.50.5 square). Total for bottom row = 1.51.5 squares.

4. Find the total unshaded area and the required fraction.

Total unshaded area = 2+1.5+1.5=52 + 1.5 + 1.5 = 5 squares.
Fraction of the figure not shaded = 59\frac{5}{9}.

Answer

59\frac{5}{9} (option 1)

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