Grade 5 Area & Perimeter Worksheet featuring geometric shapes and calculations.

To solve the problems in the "Area & Perimeter" worksheet, we need to use the formulas for calculating the area and perimeter of different shapes. Let's go through each problem step by step.

---

1. Square with side length 11 m

- Shape: Square
- Side length: 11 m

#### Area of a square:
\[
\text{Area} = \text{side}^2 = 11^2 = 121 \, \text{m}^2
\]

#### Perimeter of a square:
\[
\text{Perimeter} = 4 \times \text{side} = 4 \times 11 = 44 \, \text{m}
\]

Answer:
\[
\text{Area} = 121 \, \text{m}^2, \quad \text{Perimeter} = 44 \, \text{m}
\]

---

2. Rectangle with dimensions 12 m × 5 m

- Shape: Rectangle
- Length: 12 m
- Width: 5 m

#### Area of a rectangle:
\[
\text{Area} = \text{length} \times \text{width} = 12 \times 5 = 60 \, \text{m}^2
\]

#### Perimeter of a rectangle:
\[
\text{Perimeter} = 2 \times (\text{length} + \text{width}) = 2 \times (12 + 5) = 2 \times 17 = 34 \, \text{m}
\]

Answer:
\[
\text{Area} = 60 \, \text{m}^2, \quad \text{Perimeter} = 34 \, \text{m}
\]

---

3. Triangle with base 12 m and height 10 m

- Shape: Triangle
- Base: 12 m
- Height: 10 m

#### Area of a triangle:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 12 \times 10 = 6 \times 10 = 60 \, \text{m}^2
\]

(Note: The perimeter cannot be calculated without knowing the lengths of all three sides of the triangle.)

Answer:
\[
\text{Area} = 60 \, \text{m}^2
\]

---

4. Square with side length 5 m

- Shape: Square
- Side length: 5 m

#### Area of a square:
\[
\text{Area} = \text{side}^2 = 5^2 = 25 \, \text{m}^2
\]

#### Perimeter of a square:
\[
\text{Perimeter} = 4 \times \text{side} = 4 \times 5 = 20 \, \text{m}
\]

Answer:
\[
\text{Area} = 25 \, \text{m}^2, \quad \text{Perimeter} = 20 \, \text{m}
\]

---

5. Triangle with base 8 m and height 7 m

- Shape: Triangle
- Base: 8 m
- Height: 7 m

#### Area of a triangle:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 7 = 4 \times 7 = 28 \, \text{m}^2
\]

(Note: The perimeter cannot be calculated without knowing the lengths of all three sides of the triangle.)

Answer:
\[
\text{Area} = 28 \, \text{m}^2
\]

---

6. Rectangle with dimensions 9 m × 3 m

- Shape: Rectangle
- Length: 9 m
- Width: 3 m

#### Area of a rectangle:
\[
\text{Area} = \text{length} \times \text{width} = 9 \times 3 = 27 \, \text{m}^2
\]

#### Perimeter of a rectangle:
\[
\text{Perimeter} = 2 \times (\text{length} + \text{width}) = 2 \times (9 + 3) = 2 \times 12 = 24 \, \text{m}
\]

Answer:
\[
\text{Area} = 27 \, \text{m}^2, \quad \text{Perimeter} = 24 \, \text{m}
\]

---

7. Square with side length 9 m

- Shape: Square
- Side length: 9 m

#### Area of a square:
\[
\text{Area} = \text{side}^2 = 9^2 = 81 \, \text{m}^2
\]

#### Perimeter of a square:
\[
\text{Perimeter} = 4 \times \text{side} = 4 \times 9 = 36 \, \text{m}
\]

Answer:
\[
\text{Area} = 81 \, \text{m}^2, \quad \text{Perimeter} = 36 \, \text{m}
\]

---

8. Triangle with base 10 m and height 6 m

- Shape: Triangle
- Base: 10 m
- Height: 6 m

#### Area of a triangle:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 10 \times 6 = 5 \times 6 = 30 \, \text{m}^2
\]

(Note: The perimeter cannot be calculated without knowing the lengths of all three sides of the triangle.)

Answer:
\[
\text{Area} = 30 \, \text{m}^2
\]

---

Final Answers

\[
\boxed{
\begin{array}{ll}
1. & \text{Area} = 121 \, \text{m}^2, \, \text{Perimeter} = 44 \, \text{m} \\
2. & \text{Area} = 60 \, \text{m}^2, \, \text{Perimeter} = 34 \, \text{m} \\
3. & \text{Area} = 60 \, \text{m}^2 \\
4. & \text{Area} = 25 \, \text{m}^2, \, \text{Perimeter} = 20 \, \text{m} \\
5. & \text{Area} = 28 \, \text{m}^2 \\
6. & \text{Area} = 27 \, \text{m}^2, \, \text{Perimeter} = 24 \, \text{m} \\
7. & \text{Area} = 81 \, \text{m}^2, \, \text{Perimeter} = 36 \, \text{m} \\
8. & \text{Area} = 30 \, \text{m}^2 \\
\end{array}
}
\]