Question

what percent is represented by the 10 × 10 grid?

Explanation:

Step1: Count total squares

A 10x10 grid has \(10\times10 = 100\) squares.

Step2: Count blue squares

Let's count the blue squares. The blue region: first 6 columns (wait, let's check rows and columns. Let's see the grid:

Looking at the grid, the blue part: Let's count row by row.

Row 1: 7 blue (columns 1 - 7)
Row 2: 7 blue
Row 3: 7 blue
Row 4: 7 blue
Row 5: 7 blue
Row 6: 6 blue (column 7 is white here? Wait, no, maybe my initial count was wrong. Wait, let's re - examine.

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

First, the left - most 6 columns? No, wait, looking at the image:

Let's count the number of blue squares. Let's do it properly.

Let's consider the columns:

Columns 1 - 6: all 10 rows are blue? Wait, no. Wait, row 6 (from top, maybe row 1 is top) in column 7: is it blue? Wait, maybe a better way:

Total squares = 100. Let's count the non - blue (white) squares.

White squares: Let's see the columns 7 - 10? No, column 7: let's check each row.

Row 1: columns 8 - 10: 3 white
Row 2: columns 8 - 10: 3 white
Row 3: columns 8 - 10: 3 white
Row 4: columns 8 - 10: 3 white
Row 5: columns 7 - 10: 4 white (because column 7 is white here)
Row 6: columns 7 - 10: 4 white
Row 7: columns 7 - 10: 4 white
Row 8: columns 7 - 10: 4 white
Row 9: columns 7 - 10: 4 white
Row 10: columns 7 - 10: 4 white

Wait, this is getting complicated. Wait, maybe the correct count of blue squares:

Let's count the blue squares:

First 6 columns (columns 1 - 6) have 10 rows each? No, column 7:

Wait, looking at the grid, the blue area:

Rows 1 - 5: 7 blue (columns 1 - 7)
Rows 6 - 10: 6 blue (columns 1 - 6)

So for rows 1 - 5 (5 rows): \(5\times7=35\)
For rows 6 - 10 (5 rows): \(5\times6 = 30\)
Total blue squares: \(35 + 30=65\)? Wait, no, that can't be. Wait, maybe I made a mistake.

Wait, another approach: A 10x10 grid has 100 cells. Let's count the white cells.

White cells:

Columns 7 - 10 (4 columns) and rows 1 - 5: \(5\times3 = 15\) (columns 8 - 10, 3 columns? Wait, no, column 7: in rows 1 - 5, column 7 is blue. In rows 6 - 10, column 7 is white.

So white cells:

Rows 1 - 5: columns 8 - 10: \(5\times3=15\)
Rows 6 - 10: columns 7 - 10: \(5\times4 = 20\)
Total white cells: \(15 + 20=35\)
So blue cells = total cells - white cells = \(100 - 35 = 65\)? Wait, no, that's not right. Wait, maybe my white cell count is wrong.

Wait, let's look at the grid again. Let's count the blue squares:

Looking at the image, the blue part:

First, let's count the number of blue squares by columns:

Column 1: 10 blue
Column 2: 10 blue
Column 3: 10 blue
Column 4: 10 blue
Column 5: 10 blue
Column 6: 10 blue
Column 7: 5 blue (rows 1 - 5)
Wait, no, this is confusing. Wait, maybe the correct count is 65? No, wait, let's do it step by step.

Wait, the grid is 10 rows and 10 columns. Let's count the blue cells:

Row 1: 7 blue (columns 1 - 7)
Row 2: 7 blue
Row 3: 7 blue
Row 4: 7 blue
Row 5: 7 blue
Row 6: 6 blue (column 7 is white)
Row 7: 6 blue
Row 8: 6 blue
Row 9: 6 blue
Row 10: 6 blue

Now sum these:

Rows 1 - 5: \(5\times7 = 35\)
Rows 6 - 10: \(5\times6=30\)
Total blue: \(35 + 30 = 65\)

Wait, but 65 out of 100 is 65%. But wait, maybe I made a mistake. Wait, let's check again.

Wait, maybe the blue squares are 65? Wait, no, let's count the white squares.

White squares:

Row 1: columns 8 - 10: 3
Row 2: columns 8 - 10: 3
Row 3: columns 8 - 10: 3
Row 4: columns 8 - 10: 3
Row 5: columns 8 - 10: 3
Row 6: columns 7 - 10: 4
Row 7: columns 7 - 10: 4
Row 8: columns 7 - 10: 4
Row 9: columns 7 - 10: 4
Row 10: columns 7 - 10: 4

White squares: \(5\times3+5\times4=15 + 20 = 35\)

Blue squares: \(100 - 35=65\)

So the percentage is \(\frac{65}{100}\times100 = 65\%\)

Wait, but maybe I miscounted. Wait, another way: Let's look at the grid. The blue area: the first 6 columns (columns 1 - 6) have 10 rows each (10*6 = 60), and column 7 has 5 rows (rows 1 - 5), so total blue is 60+5 = 65. Yes, that matches.

Step3: Calculate percentage

Percentage is (number of blue squares / total number of squares)×100. Since total squares = 100, the percentage is equal to the number of blue squares. So if there are 65 blue squares, the percentage is 65%.

Answer:

65