Solve multiplication problems and color the picture to reveal a hidden design in this fun math activity.

Problem Description:

The task involves solving a series of arithmetic problems (addition) and coloring the corresponding sections of a geometric pattern based on the results. Each section contains an addition problem, and the sum determines which color to use according to the provided legend.

Legend:

- Green: Sums between 0 and 10
- Pink: Sums between 11 and 20
- Blue: Sums between 31 and 40
- Red: Sums between 41 and 50

Steps to Solve:

1. Identify Each Addition Problem: Each section of the geometric pattern contains an addition problem.
2. Solve Each Problem: Calculate the sum of each addition problem.
3. Match the Sum to the Color Legend: Determine which color corresponds to the calculated sum based on the given ranges.
4. Color the Section: Fill in the section with the appropriate color.

Detailed Solution:

#### Step 1: Solve Each Addition Problem
We will solve all the addition problems one by one:

1. Top Row:
- \( 3 \times 5 = 15 \)
- \( 4 \times 9 = 36 \)
- \( 35 + 5 = 40 \)
- \( 7 \times 5 = 35 \)
- \( 7 \times 7 = 49 \)

2. Second Row:
- \( 2 \times 25 = 50 \)
- \( 6 \times 8 = 48 \)
- \( 3 \times 6 = 18 \)
- \( 2 \times 15 = 30 \)
- \( 6 \times 7 = 42 \)
- \( 4 \times 11 = 44 \)

3. Third Row:
- \( 7 \times 5 = 35 \)
- \( 4 \times 7 = 28 \)
- \( 2 \times 14 = 28 \)
- \( 5 \times 11 = 55 \)
- \( 9 \times 3 = 27 \)
- \( -3 \times 10 = -30 \)
- \( 3 \times 3 = 9 \)

4. Fourth Row:
- \( 4 \times 5 = 20 \)
- \( 6 \times 6 = 36 \)
- \( 3 \times 14 = 42 \)
- \( 80 + 4 = 84 \)
- \( 9 \times 6 = 54 \)
- \( 15 \times 3 = 45 \)
- \( 51 - 9 = 42 \)

5. Fifth Row:
- \( 6 \times 6 = 36 \)
- \( 36 + 3 = 39 \)
- \( 2 \times 23 = 46 \)
- \( 63 + 3 = 66 \)
- \( 5 \times 9 = 45 \)
- \( 8 \times 5 = 40 \)
- \( 4 \times 12 = 48 \)

#### Step 2: Match Sums to Colors
Using the legend:
- Green: 0–10
- Pink: 11–20
- Blue: 31–40
- Red: 41–50

Now, we assign colors based on the sums:

1. Top Row:
- \( 15 \): Pink
- \( 36 \): Blue
- \( 40 \): Blue
- \( 35 \): Blue
- \( 49 \): Red

2. Second Row:
- \( 50 \): Red
- \( 48 \): Red
- \( 18 \): Pink
- \( 30 \): Pink
- \( 42 \): Red
- \( 44 \): Red

3. Third Row:
- \( 35 \): Blue
- \( 28 \): Pink
- \( 28 \): Pink
- \( 55 \): Red
- \( 27 \): Pink
- \( -30 \): Green
- \( 9 \): Green

4. Fourth Row:
- \( 20 \): Pink
- \( 36 \): Blue
- \( 42 \): Red
- \( 84 \): Red
- \( 54 \): Red
- \( 45 \): Red
- \( 42 \): Red

5. Fifth Row:
- \( 36 \): Blue
- \( 39 \): Blue
- \( 46 \): Red
- \( 66 \): Red
- \( 45 \): Red
- \( 40 \): Blue
- \( 48 \): Red

#### Step 3: Color the Sections
Based on the above calculations, fill in each section with the corresponding color.

Final Answer:

The completed image would have sections colored as follows:
- Green: Sections with sums between 0 and 10.
- Pink: Sections with sums between 11 and 20.
- Blue: Sections with sums between 31 and 40.
- Red: Sections with sums between 41 and 50.

Since I cannot physically color the image here, the final answer is the process and the color assignments for each section. If you need a visual representation, you can manually color the sections based on the provided sums and legend.

\boxed{\text{See the detailed color assignments above.}}