Grade 5 Area & Perimeter Worksheet with problems for calculating area and perimeter of rectangles and squares.

Problem: Solve the area and perimeter for each shape in the worksheet.

#### Definitions:
- Area of a Rectangle/Square:
- Rectangle: \( \text{Area} = \text{length} \times \text{width} \)
- Square: \( \text{Area} = \text{side} \times \text{side} \)

- Perimeter of a Rectangle/Square:
- Rectangle: \( \text{Perimeter} = 2 \times (\text{length} + \text{width}) \)
- Square: \( \text{Perimeter} = 4 \times \text{side} \)

---

Step-by-Step Solution:

#### 1. Rectangle (8m × 5m)
- Area:
\[
\text{Area} = \text{length} \times \text{width} = 8 \, \text{m} \times 5 \, \text{m} = 40 \, \text{m}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (\text{length} + \text{width}) = 2 \times (8 \, \text{m} + 5 \, \text{m}) = 2 \times 13 \, \text{m} = 26 \, \text{m}
\]

#### 2. Square (6m × 6m)
- Area:
\[
\text{Area} = \text{side} \times \text{side} = 6 \, \text{m} \times 6 \, \text{m} = 36 \, \text{m}^2
\]
- Perimeter:
\[
\text{Perimeter} = 4 \times \text{side} = 4 \times 6 \, \text{m} = 24 \, \text{m}
\]

#### 3. Rectangle (12m × 3m)
- Area:
\[
\text{Area} = \text{length} \times \text{width} = 12 \, \text{m} \times 3 \, \text{m} = 36 \, \text{m}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (\text{length} + \text{width}) = 2 \times (12 \, \text{m} + 3 \, \text{m}) = 2 \times 15 \, \text{m} = 30 \, \text{m}
\]

#### 4. Rectangle (7m × 6m)
- Area:
\[
\text{Area} = \text{length} \times \text{width} = 7 \, \text{m} \times 6 \, \text{m} = 42 \, \text{m}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (\text{length} + \text{width}) = 2 \times (7 \, \text{m} + 6 \, \text{m}) = 2 \times 13 \, \text{m} = 26 \, \text{m}
\]

#### 5. Square (6m × 6m)
- Area:
\[
\text{Area} = \text{side} \times \text{side} = 6 \, \text{m} \times 6 \, \text{m} = 36 \, \text{m}^2
\]
- Perimeter:
\[
\text{Perimeter} = 4 \times \text{side} = 4 \times 6 \, \text{m} = 24 \, \text{m}
\]

#### 6. Rectangle (15m × 5m)
- Area:
\[
\text{Area} = \text{length} \times \text{width} = 15 \, \text{m} \times 5 \, \text{m} = 75 \, \text{m}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (\text{length} + \text{width}) = 2 \times (15 \, \text{m} + 5 \, \text{m}) = 2 \times 20 \, \text{m} = 40 \, \text{m}
\]

#### 7. Rectangle (8m × 7m)
- Area:
\[
\text{Area} = \text{length} \times \text{width} = 8 \, \text{m} \times 7 \, \text{m} = 56 \, \text{m}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (\text{length} + \text{width}) = 2 \times (8 \, \text{m} + 7 \, \text{m}) = 2 \times 15 \, \text{m} = 30 \, \text{m}
\]

#### 8. Square (9m × 9m)
- Area:
\[
\text{Area} = \text{side} \times \text{side} = 9 \, \text{m} \times 9 \, \text{m} = 81 \, \text{m}^2
\]
- Perimeter:
\[
\text{Perimeter} = 4 \times \text{side} = 4 \times 9 \, \text{m} = 36 \, \text{m}
\]

---

Final Answers:

1. Rectangle (8m × 5m)
- Area: \( 40 \, \text{m}^2 \)
- Perimeter: \( 26 \, \text{m} \)

2. Square (6m × 6m)
- Area: \( 36 \, \text{m}^2 \)
- Perimeter: \( 24 \, \text{m} \)

3. Rectangle (12m × 3m)
- Area: \( 36 \, \text{m}^2 \)
- Perimeter: \( 30 \, \text{m} \)

4. Rectangle (7m × 6m)
- Area: \( 42 \, \text{m}^2 \)
- Perimeter: \( 26 \, \text{m} \)

5. Square (6m × 6m)
- Area: \( 36 \, \text{m}^2 \)
- Perimeter: \( 24 \, \text{m} \)

6. Rectangle (15m × 5m)
- Area: \( 75 \, \text{m}^2 \)
- Perimeter: \( 40 \, \text{m} \)

7. Rectangle (8m × 7m)
- Area: \( 56 \, \text{m}^2 \)
- Perimeter: \( 30 \, \text{m} \)

8. Square (9m × 9m)
- Area: \( 81 \, \text{m}^2 \)
- Perimeter: \( 36 \, \text{m} \)

---

Boxed Final Answer:

\[
\boxed{
\begin{array}{ll}
1. & \text{Area: } 40 \, \text{m}^2, \text{ Perimeter: } 26 \, \text{m} \\
2. & \text{Area: } 36 \, \text{m}^2, \text{ Perimeter: } 24 \, \text{m} \\
3. & \text{Area: } 36 \, \text{m}^2, \text{ Perimeter: } 30 \, \text{m} \\
4. & \text{Area: } 42 \, \text{m}^2, \text{ Perimeter: } 26 \, \text{m} \\
5. & \text{Area: } 36 \, \text{m}^2, \text{ Perimeter: } 24 \, \text{m} \\
6. & \text{Area: } 75 \, \text{m}^2, \text{ Perimeter: } 40 \, \text{m} \\
7. & \text{Area: } 56 \, \text{m}^2, \text{ Perimeter: } 30 \, \text{m} \\
8. & \text{Area: } 81 \, \text{m}^2, \text{ Perimeter: } 36 \, \text{m} \\
\end{array}
}
\]