Area model multiplication worksheet for two-digit by two-digit multiplication, featuring a solved example and five practice problems with empty grids.

To solve the problems using the area model for multiplication, we will break each two-digit number into tens and ones, then multiply the parts systematically. Let's go through each problem step by step.

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Problem b: \( 78 \times 58 \)

#### Step 1: Break down the numbers
- \( 78 = 70 + 8 \)
- \( 58 = 50 + 8 \)

#### Step 2: Set up the area model
We will create a 2x2 grid:
\[
\begin{array}{c|c|c}
& 50 & 8 \\
\hline
70 & 70 \times 50 & 70 \times 8 \\
\hline
8 & 8 \times 50 & 8 \times 8 \\
\end{array}
\]

#### Step 3: Calculate each part
1. \( 70 \times 50 = 3500 \)
2. \( 70 \times 8 = 560 \)
3. \( 8 \times 50 = 400 \)
4. \( 8 \times 8 = 64 \)

#### Step 4: Add the products
\[
3500 + 560 + 400 + 64 = 4524
\]

#### Final Answer:
\[
\boxed{4524}
\]

---

Problem c: \( 85 \times 12 \)

#### Step 1: Break down the numbers
- \( 85 = 80 + 5 \)
- \( 12 = 10 + 2 \)

#### Step 2: Set up the area model
We will create a 2x2 grid:
\[
\begin{array}{c|c|c}
& 10 & 2 \\
\hline
80 & 80 \times 10 & 80 \times 2 \\
\hline
5 & 5 \times 10 & 5 \times 2 \\
\end{array}
\]

#### Step 3: Calculate each part
1. \( 80 \times 10 = 800 \)
2. \( 80 \times 2 = 160 \)
3. \( 5 \times 10 = 50 \)
4. \( 5 \times 2 = 10 \)

#### Step 4: Add the products
\[
800 + 160 + 50 + 10 = 1020
\]

#### Final Answer:
\[
\boxed{1020}
\]

---

Problem d: \( 82 \times 53 \)

#### Step 1: Break down the numbers
- \( 82 = 80 + 2 \)
- \( 53 = 50 + 3 \)

#### Step 2: Set up the area model
We will create a 2x2 grid:
\[
\begin{array}{c|c|c}
& 50 & 3 \\
\hline
80 & 80 \times 50 & 80 \times 3 \\
\hline
2 & 2 \times 50 & 2 \times 3 \\
\end{array}
\]

#### Step 3: Calculate each part
1. \( 80 \times 50 = 4000 \)
2. \( 80 \times 3 = 240 \)
3. \( 2 \times 50 = 100 \)
4. \( 2 \times 3 = 6 \)

#### Step 4: Add the products
\[
4000 + 240 + 100 + 6 = 4346
\]

#### Final Answer:
\[
\boxed{4346}
\]

---

Problem e: \( 35 \times 18 \)

#### Step 1: Break down the numbers
- \( 35 = 30 + 5 \)
- \( 18 = 10 + 8 \)

#### Step 2: Set up the area model
We will create a 2x2 grid:
\[
\begin{array}{c|c|c}
& 10 & 8 \\
\hline
30 & 30 \times 10 & 30 \times 8 \\
\hline
5 & 5 \times 10 & 5 \times 8 \\
\end{array}
\]

#### Step 3: Calculate each part
1. \( 30 \times 10 = 300 \)
2. \( 30 \times 8 = 240 \)
3. \( 5 \times 10 = 50 \)
4. \( 5 \times 8 = 40 \)

#### Step 4: Add the products
\[
300 + 240 + 50 + 40 = 630
\]

#### Final Answer:
\[
\boxed{630}
\]

---

Problem f: \( 11 \times 28 \)

#### Step 1: Break down the numbers
- \( 11 = 10 + 1 \)
- \( 28 = 20 + 8 \)

#### Step 2: Set up the area model
We will create a 2x2 grid:
\[
\begin{array}{c|c|c}
& 20 & 8 \\
\hline
10 & 10 \times 20 & 10 \times 8 \\
\hline
1 & 1 \times 20 & 1 \times 8 \\
\end{array}
\]

#### Step 3: Calculate each part
1. \( 10 \times 20 = 200 \)
2. \( 10 \times 8 = 80 \)
3. \( 1 \times 20 = 20 \)
4. \( 1 \times 8 = 8 \)

#### Step 4: Add the products
\[
200 + 80 + 20 + 8 = 308
\]

#### Final Answer:
\[
\boxed{308}
\]

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Summary of Answers

\[
\boxed{4524, 1020, 4346, 630, 308}
\]