Question

the figure below is divided into 100 squares of equal size. what percent of the figure is shaded?

Explanation:

Step1: Count shaded squares

First, we count the number of shaded squares. Let's analyze the grid:
- The first part (top) has a 4x4 square? Wait, no, let's look row by row. Wait, the grid is 10x10 (since 100 squares total, 10 rows and 10 columns). Let's count the shaded cells:
Looking at the figure, let's count:
Row 2 (assuming row 1 is top): 4 shaded (columns 2 - 5)
Row 3: 4 shaded (columns 2 - 5)
Row 4: 4 shaded (columns 2 - 5)
Row 5: 4 shaded (columns 2 - 5)
Row 6: 9 shaded (columns 2 - 10? Wait, no, let's check again. Wait, maybe a better way: the unshaded columns are column 1 and column 10? Wait, no, looking at the grid, the first column (leftmost) and the last column (rightmost) have some unshaded? Wait, no, let's count the shaded cells:

Wait, the grid is 10 columns (x - axis) and 10 rows (y - axis). Let's count the shaded cells:

Columns: Let's see, column 2 to column 9 (8 columns) and rows: let's see, row 2 to row 9 (8 rows)? Wait, no, maybe I made a mistake. Wait, the total number of squares is 100. Let's count the shaded ones:

Looking at the figure, the shaded area:

From column 2 to column 9 (8 columns) and row 2 to row 9 (8 rows)? No, wait, let's count:

Wait, the first row (top) has 0 shaded? No, row 1 (top) has all unshaded? Wait, row 1: all white. Row 2: columns 2 - 5 (4 shaded). Row 3: columns 2 - 5 (4). Row 4: columns 2 - 5 (4). Row 5: columns 2 - 5 (4). Then row 6: columns 2 - 9 (8 shaded). Row 7: columns 2 - 9 (8). Row 8: columns 2 - 9 (8). Row 9: columns 2 - 9 (8). Row 10: columns 2 - 9 (8). Wait, no, that can't be. Wait, maybe the unshaded cells are column 1 (all rows) and column 10 (all rows) except some? Wait, no, let's count:

Wait, column 1 (leftmost) has 10 unshaded? No, column 1: row 1 - 10, all unshaded? No, the figure shows that column 1 (first column) has some unshaded, and column 10 (last column) has some unshaded. Wait, maybe a better approach: the number of unshaded squares. Let's count unshaded:

Column 1 (10 rows): all unshaded? No, row 1: column 1 is unshaded, row 2: column 1 is unshaded, ..., row 10: column 1 is unshaded. So column 1: 10 unshaded.

Column 10 (10 rows): row 1: unshaded, row 2: unshaded, ..., row 10: unshaded? Wait, no, in row 6 - 10, column 10: is it shaded? Wait, the figure shows that in row 6 - 10, column 10 is unshaded? Wait, maybe I'm overcomplicating. Wait, the total number of squares is 100. Let's count the shaded ones:

Looking at the figure, the shaded area:

From column 2 to column 9 (8 columns) and row 2 to row 10 (9 rows)? No, row 1: column 2 - 9: unshaded. So row 1: 0 shaded.

Row 2: column 2 - 5: 4 shaded.

Row 3: column 2 - 5: 4 shaded.

Row 4: column 2 - 5: 4 shaded.

Row 5: column 2 - 5: 4 shaded.

Row 6: column 2 - 9: 8 shaded.

Row 7: column 2 - 9: 8 shaded.

Row 8: column 2 - 9: 8 shaded.

Row 9: column 2 - 9: 8 shaded.

Row 10: column 2 - 9: 8 shaded.

Now let's calculate:

Rows 2 - 5: 4 rows × 4 shaded = 16

Rows 6 - 10: 5 rows × 8 shaded = 40

Total shaded: 16 + 40 = 56? Wait, no, that can't be. Wait, maybe I made a mistake. Wait, row 2 - 5: 4 rows, each with 4 shaded: 4×4=16. Rows 6 - 10: 5 rows, each with 8 shaded: 5×8=40. 16+40=56? But wait, let's check again. Wait, maybe the unshaded columns are column 1 and column 10, so 8 columns (2 - 9) and rows: let's see, row 1: column 2 - 9: unshaded (0). Rows 2 - 5: column 2 - 5: 4 per row (4 rows: 16). Rows 6 - 10: column 2 - 9: 8 per row (5 rows: 40). Total: 16 + 40 = 56? Wait, but 56 out of 100 is 56%. But wait, maybe I miscounted. Wait, another way: the total number of squares is 100. Let's count the unshaded squares:

Column 1: 10 squares (all unshaded)

Column 10: let's see, rows 1 - 5: column 10 is unshaded (5 squares), rows 6 - 10: column 10 is unshaded? Wait, no, in row 6 - 10, column 10: is it shaded? Looking at the figure, the rightmost column (column 10) has unshaded in row 1 - 5, and shaded in row 6 - 10? No, the figure shows that the rightmost column (column 10) has some unshaded. Wait, maybe my initial approach is wrong. Let's count the shaded squares properly:

Looking at the grid, the shaded area:

- The top part: a 4x4 square? No, 4 columns (2 - 5) and 4 rows (2 - 5): 4×4=16.

- The bottom part: from row 6 to row 10 (5 rows) and columns 2 to 9 (8 columns): 5×8=40.

Total shaded: 16 + 40 = 56. So 56 out of 100, which is 56%. Wait, but let's confirm. 100 squares total. If 56 are shaded, then the percentage is (56/100)×100 = 56%.

Wait, maybe I made a mistake in counting. Let's check again:

Row 1 (top row): all unshaded (0 shaded)

Row 2: columns 2,3,4,5 (4 shaded)

Row 3: columns 2,3,4,5 (4 shaded)

Row 4: columns 2,3,4,5 (4 shaded)

Row 5: columns 2,3,4,5 (4 shaded)

Row 6: columns 2,3,4,5,6,7,8,9 (8 shaded)

Row 7: columns 2,3,4,5,6,7,8,9 (8 shaded)

Row 8: columns 2,3,4,5,6,7,8,9 (8 shaded)

Row 9: columns 2,3,4,5,6,7,8,9 (8 shaded)

Row 10: columns 2,3,4,5,6,7,8,9 (8 shaded)

Now sum the shaded:

Row 2: 4

Row 3: 4 (total 8)

Row 4: 4 (total 12)

Row 5: 4 (total 16)

Row 6: 8 (total 24)

Row 7: 8 (total 32)

Row 8: 8 (total 40)

Row 9: 8 (total 48)

Row 10: 8 (total 56)

Yes, that's 56 shaded squares.

Step2: Calculate percentage

To find the percentage, we use the formula:

Percentage = (Number of shaded squares / Total number of squares) × 100

We know the number of shaded squares is 56, and the total number of squares is 100.

So, Percentage = (56 / 100) × 100 = 56%

Answer:

56%