Students calculate the area and perimeter of various L-shaped and T-shaped compound figures using the given dimensions in centimeters.

To solve the problems involving compound shapes, we need to calculate both the area and the perimeter for each shape. Let's go through each problem step by step.

---

Problem 1:

#### Shape:
- Rectangle (A): \(4 \, \text{cm} \times 3 \, \text{cm}\)
- Rectangle (B): \(8 \, \text{cm} \times 3 \, \text{cm}\)

#### Calculations:
1. Area of Rectangle (A):
\[
\text{Area} = \text{length} \times \text{width} = 4 \, \text{cm} \times 3 \, \text{cm} = 12 \, \text{cm}^2
\]

2. Area of Rectangle (B):
\[
\text{Area} = \text{length} \times \text{width} = 8 \, \text{cm} \times 3 \, \text{cm} = 24 \, \text{cm}^2
\]

3. Total Area:
\[
\text{Total Area} = \text{Area of (A)} + \text{Area of (B)} = 12 \, \text{cm}^2 + 24 \, \text{cm}^2 = 36 \, \text{cm}^2
\]

4. Perimeter:
- The perimeter is the sum of all outer sides.
- Top side: \(8 \, \text{cm}\)
- Bottom side: \(8 \, \text{cm}\)
- Left side: \(6 \, \text{cm}\)
- Right side: \(6 \, \text{cm}\)
- Inner vertical side: \(3 \, \text{cm}\) (shared between A and B)
\[
\text{Perimeter} = 8 + 8 + 6 + 6 + 3 = 31 \, \text{cm}
\]

#### Answers:
- Area of rectangle (A): \(12 \, \text{cm}^2\)
- Area of rectangle (B): \(24 \, \text{cm}^2\)
- Total area: \(36 \, \text{cm}^2\)
- Perimeter: \(31 \, \text{cm}\)

---

Problem 2:

#### Shape:
- Rectangle (A): \(7 \, \text{cm} \times 1 \, \text{cm}\)
- Rectangle (B): \(6 \, \text{cm} \times 4 \, \text{cm}\)

#### Calculations:
1. Area of Rectangle (A):
\[
\text{Area} = \text{length} \times \text{width} = 7 \, \text{cm} \times 1 \, \text{cm} = 7 \, \text{cm}^2
\]

2. Area of Rectangle (B):
\[
\text{Area} = \text{length} \times \text{width} = 6 \, \text{cm} \times 4 \, \text{cm} = 24 \, \text{cm}^2
\]

3. Total Area:
\[
\text{Total Area} = \text{Area of (A)} + \text{Area of (B)} = 7 \, \text{cm}^2 + 24 \, \text{cm}^2 = 31 \, \text{cm}^2
\]

4. Perimeter:
- The perimeter is the sum of all outer sides.
- Top side: \(7 \, \text{cm}\)
- Bottom side: \(7 \, \text{cm}\)
- Left side: \(1 \, \text{cm} + 6 \, \text{cm} = 7 \, \text{cm}\)
- Right side: \(4 \, \text{cm}\)
- Inner horizontal side: \(3 \, \text{cm}\) (shared between A and B)
\[
\text{Perimeter} = 7 + 7 + 7 + 4 + 3 = 28 \, \text{cm}
\]

#### Answers:
- Area of rectangle (A): \(7 \, \text{cm}^2\)
- Area of rectangle (B): \(24 \, \text{cm}^2\)
- Total area: \(31 \, \text{cm}^2\)
- Perimeter: \(28 \, \text{cm}\)

---

Problem 3:

#### Shape:
- Rectangle (A): \(2 \, \text{cm} \times 10 \, \text{cm}\)
- Rectangle (B): \(7 \, \text{cm} \times 3 \, \text{cm}\)

#### Calculations:
1. Area of Rectangle (A):
\[
\text{Area} = \text{length} \times \text{width} = 2 \, \text{cm} \times 10 \, \text{cm} = 20 \, \text{cm}^2
\]

2. Area of Rectangle (B):
\[
\text{Area} = \text{length} \times \text{width} = 7 \, \text{cm} \times 3 \, \text{cm} = 21 \, \text{cm}^2
\]

3. Total Area:
\[
\text{Total Area} = \text{Area of (A)} + \text{Area of (B)} = 20 \, \text{cm}^2 + 21 \, \text{cm}^2 = 41 \, \text{cm}^2
\]

4. Perimeter:
- The perimeter is the sum of all outer sides.
- Top side: \(9 \, \text{cm}\)
- Bottom side: \(9 \, \text{cm}\)
- Left side: \(2 \, \text{cm} + 7 \, \text{cm} = 9 \, \text{cm}\)
- Right side: \(3 \, \text{cm}\)
- Inner horizontal side: \(7 \, \text{cm}\) (shared between A and B)
\[
\text{Perimeter} = 9 + 9 + 9 + 3 + 7 = 37 \, \text{cm}
\]

#### Answers:
- Area of rectangle (A): \(20 \, \text{cm}^2\)
- Area of rectangle (B): \(21 \, \text{cm}^2\)
- Total area: \(41 \, \text{cm}^2\)
- Perimeter: \(37 \, \text{cm}\)

---

Problem 4:

#### Shape:
- Top rectangle: \(12 \, \text{cm} \times 4 \, \text{cm}\)
- Bottom rectangle: \(5 \, \text{cm} \times 9 \, \text{cm}\)

#### Calculations:
1. Area of Top Rectangle:
\[
\text{Area} = \text{length} \times \text{width} = 12 \, \text{cm} \times 4 \, \text{cm} = 48 \, \text{cm}^2
\]

2. Area of Bottom Rectangle:
\[
\text{Area} = \text{length} \times \text{width} = 5 \, \text{cm} \times 9 \, \text{cm} = 45 \, \text{cm}^2
\]

3. Total Area:
\[
\text{Total Area} = \text{Area of Top Rectangle} + \text{Area of Bottom Rectangle} = 48 \, \text{cm}^2 + 45 \, \text{cm}^2 = 93 \, \text{cm}^2
\]

4. Perimeter:
- The perimeter is the sum of all outer sides.
- Top side: \(12 \, \text{cm}\)
- Bottom side: \(5 \, \text{cm} + 2 \, \text{cm} + 5 \, \text{cm} = 12 \, \text{cm}\)
- Left side: \(4 \, \text{cm} + 9 \, \text{cm} = 13 \, \text{cm}\)
- Right side: \(4 \, \text{cm} + 9 \, \text{cm} = 13 \, \text{cm}\)
\[
\text{Perimeter} = 12 + 12 + 13 + 13 = 50 \, \text{cm}
\]

#### Answers:
- Total area: \(93 \, \text{cm}^2\)
- Perimeter: \(50 \, \text{cm}\)

---

Problem 5:

#### Shape:
- Large rectangle: \(15 \, \text{cm} \times 11 \, \text{cm}\)
- Small rectangle: \(7 \, \text{cm} \times 6 \, \text{cm}\)

#### Calculations:
1. Area of Large Rectangle:
\[
\text{Area} = \text{length} \times \text{width} = 15 \, \text{cm} \times 11 \, \text{cm} = 165 \, \text{cm}^2
\]

2. Area of Small Rectangle:
\[
\text{Area} = \text{length} \times \text{width} = 7 \, \text{cm} \times 6 \, \text{cm} = 42 \, \text{cm}^2
\]

3. Total Area:
\[
\text{Total Area} = \text{Area of Large Rectangle} - \text{Area of Small Rectangle} = 165 \, \text{cm}^2 - 42 \, \text{cm}^2 = 123 \, \text{cm}^2
\]

4. Perimeter:
- The perimeter is the sum of all outer sides.
- Top side: \(15 \, \text{cm}\)
- Bottom side: \(15 \, \text{cm}\)
- Left side: \(11 \, \text{cm}\)
- Right side: \(11 \, \text{cm}\)
\[
\text{Perimeter} = 15 + 15 + 11 + 11 = 52 \, \text{cm}
\]

#### Answers:
- Total area: \(123 \, \text{cm}^2\)
- Perimeter: \(52 \, \text{cm}\)

---

Problem 6:

#### Shape:
- Top rectangle: \(13 \, \text{cm} \times 2 \, \text{cm}\)
- Middle rectangle: \(10 \, \text{cm} \times 7 \, \text{cm}\)
- Bottom rectangle: \(5 \, \text{cm} \times 3 \, \text{cm}\)

#### Calculations:
1. Area of Top Rectangle:
\[
\text{Area} = \text{length} \times \text{width} = 13 \, \text{cm} \times 2 \, \text{cm} = 26 \, \text{cm}^2
\]

2. Area of Middle Rectangle:
\[
\text{Area} = \text{length} \times \text{width} = 10 \, \text{cm} \times 7 \, \text{cm} = 70 \, \text{cm}^2
\]

3. Area of Bottom Rectangle:
\[
\text{Area} = \text{length} \times \text{width} = 5 \, \text{cm} \times 3 \, \text{cm} = 15 \, \text{cm}^2
\]

4. Total Area:
\[
\text{Total Area} = \text{Area of Top Rectangle} + \text{Area of Middle Rectangle} + \text{Area of Bottom Rectangle} = 26 \, \text{cm}^2 + 70 \, \text{cm}^2 + 15 \, \text{cm}^2 = 111 \, \text{cm}^2
\]

5. Perimeter:
- The perimeter is the sum of all outer sides.
- Top side: \(13 \, \text{cm}\)
- Bottom side: \(5 \, \text{cm} + 3 \, \text{cm} + 5 \, \text{cm} = 13 \, \text{cm}\)
- Left side: \(2 \, \text{cm} + 7 \, \text{cm} + 3 \, \text{cm} = 12 \, \text{cm}\)
- Right side: \(2 \, \text{cm} + 7 \, \text{cm} + 3 \, \text{cm} = 12 \, \text{cm}\)
\[
\text{Perimeter} = 13 + 13 + 12 + 12 = 50 \, \text{cm}
\]

#### Answers:
- Total area: \(111 \, \text{cm}^2\)
- Perimeter: \(50 \, \text{cm}\)

---

Final Answers:

1.
- Area of rectangle (A): \(12 \, \text{cm}^2\)
- Area of rectangle (B): \(24 \, \text{cm}^2\)
- Total area: \(36 \, \text{cm}^2\)
- Perimeter: \(31 \, \text{cm}\)

2.
- Area of rectangle (A): \(7 \, \text{cm}^2\)
- Area of rectangle (B): \(24 \, \text{cm}^2\)
- Total area: \(31 \, \text{cm}^2\)
- Perimeter: \(28 \, \text{cm}\)

3.
- Area of rectangle (A): \(20 \, \text{cm}^2\)
- Area of rectangle (B): \(21 \, \text{cm}^2\)
- Total area: \(41 \, \text{cm}^2\)
- Perimeter: \(37 \, \text{cm}\)

4.
- Total area: \(93 \, \text{cm}^2\)
- Perimeter: \(50 \, \text{cm}\)

5.
- Total area: \(123 \, \text{cm}^2\)
- Perimeter: \(52 \, \text{cm}\)

6.
- Total area: \(111 \, \text{cm}^2\)
- Perimeter: \(50 \, \text{cm}\)

\boxed{
\begin{array}{l}
\text{1. Total area: } 36 \, \text{cm}^2, \text{ Perimeter: } 31 \, \text{cm} \\
\text{2. Total area: } 31 \, \text{cm}^2, \text{ Perimeter: } 28 \, \text{cm} \\
\text{3. Total area: } 41 \, \text{cm}^2, \text{ Perimeter: } 37 \, \text{cm} \\
\text{4. Total area: } 93 \, \text{cm}^2, \text{ Perimeter: } 50 \, \text{cm} \\
\text{5. Total area: } 123 \, \text{cm}^2, \text{ Perimeter: } 52 \, \text{cm} \\
\text{6. Total area: } 111 \, \text{cm}^2, \text{ Perimeter: } 50 \, \text{cm}
\end{array}
}