Question

spiral review
problems 9–10: determine the percentage of each grid that is shaded.
(9. grid with shaded squares

1. grid with shaded squares and triangles)

Explanation:

Step1: Analyze Grid 9

The grid has 5 rows and 5 columns, so total cells = \(5\times5 = 25\). Shaded cells: 4 rows (each with 2 cells) = \(4\times2 = 8\)? Wait, no, looking at the grid: columns 4 and 5 (2 columns), rows 1 - 4 (4 rows) are shaded. So shaded cells: \(4\times2 = 8\)? Wait, no, 5 rows: row 1 - 4 (4 rows) have 2 shaded each, row 5 has 0. Wait, no, the grid is 5x5. Let's count:

Row 1: 2 shaded (cols 4,5)
Row 2: 2 shaded
Row 3: 2 shaded
Row 4: 2 shaded
Row 5: 0 shaded
Total shaded: \(4\times2 = 8\)? Wait, no, 5 rows, 5 columns. Wait, 5 columns: cols 1 - 3 (white), cols 4 - 5 (shaded) for rows 1 - 4, row 5 cols 4 - 5 are white. So rows 1 - 4: 2 cols each, so 4*2=8. Total cells: 25. So percentage: \(\frac{8}{25}\times100 = 32\%\).

Step2: Analyze Grid 10

Total cells: 5x5=25. Let's count shaded areas:

• Full squares: Let's see:
• Row 1: cols 2 - 4 (3)
• Row 2: col 4 (1)
• Row 3: col 2 (1)
• Row 4: col 4 (1)
• Triangles: Two triangles, each is half a square. So two triangles = 1 full square.

Wait, let's list:

Row 1: cols 2,3,4 (3 full)
Row 2: col 4 (1 full)
Row 3: col 2 (1 full)
Row 4: col 4 (1 full)
Row 5: col 3 (half, triangle) and col 2 (half, triangle) → total 1 full.

Wait, let's count:

Full squares: 3 (row1) +1 (row2) +1 (row3) +1 (row4) = 6.

Triangles: row4 col2: half, row5 col3: half. So 0.5 + 0.5 = 1.

Total shaded: 6 + 1 = 7? Wait, no, maybe better to count each cell:

Each cell is 1 unit. Triangles: each triangle is half a cell.

Let's list each cell:

Row 1:

• Col1: white
• Col2: full (shaded)
• Col3: full (shaded)
• Col4: full (shaded)
• Col5: white

→ 3 full.

Row 2:

• Col1: white
• Col2: white
• Col3: white
• Col4: full (shaded)
• Col5: white

→ 1 full.

Row 3:

• Col1: white
• Col2: full (shaded)
• Col3: white
• Col4: white
• Col5: white

→ 1 full.

Row 4:

• Col1: white
• Col2: half (triangle, shaded)
• Col3: white
• Col4: full (shaded)
• Col5: white

→ 0.5 + 1 = 1.5.

Row 5:

• Col1: white
• Col2: white
• Col3: half (triangle, shaded)
• Col4: white
• Col5: white

→ 0.5.

Now sum:

Row1: 3

Row2: 1 → total 4

Row3: 1 → total 5

Row4: 1.5 → total 6.5

Row5: 0.5 → total 7.

So total shaded: 7. Total cells:25. Percentage: \(\frac{7}{25}\times100 = 28\%\). Wait, but let's check again.

Wait, row4 col2: triangle (half), row5 col3: triangle (half). So two triangles = 1 full. Then full squares:

Row1: 3

Row2: 1

Row3: 1

Row4: 1 (col4)

Row5: 0

Plus 1 (from two triangles) → total 3+1+1+1+1=7. Yes. So 7/25=28%.

Answer:

Grid 9: 32%
Grid 10: 28%