Grade 5 Area and Perimeter Worksheet featuring six irregular shapes with labeled dimensions for calculating area and perimeter.

To solve the problems related to the Area and Perimeter of the given shapes, we will calculate each one step by step. Let's go through each problem:

---

Problem 1:

#### Shape:
- A rectangle with dimensions \(10 \, \text{m} \times 10 \, \text{m}\).

#### Calculations:
1. Area:
\[
\text{Area} = \text{length} \times \text{width} = 10 \, \text{m} \times 10 \, \text{m} = 100 \, \text{m}^2
\]

2. Perimeter:
\[
\text{Perimeter} = 2 \times (\text{length} + \text{width}) = 2 \times (10 \, \text{m} + 10 \, \text{m}) = 2 \times 20 \, \text{m} = 40 \, \text{m}
\]

#### Answers:
- Area: \(100 \, \text{m}^2\)
- Perimeter: \(40 \, \text{m}\)

---

Problem 2:

#### Shape:
- A composite shape consisting of two rectangles:
- Top rectangle: \(9 \, \text{m} \times 5 \, \text{m}\)
- Bottom rectangle: \(3 \, \text{m} \times 5 \, \text{m}\)

#### Calculations:
1. Area:
- Area of top rectangle: \(9 \, \text{m} \times 5 \, \text{m} = 45 \, \text{m}^2\)
- Area of bottom rectangle: \(3 \, \text{m} \times 5 \, \text{m} = 15 \, \text{m}^2\)
- Total area: \(45 \, \text{m}^2 + 15 \, \text{m}^2 = 60 \, \text{m}^2\)

2. Perimeter:
- The shape has the following outer sides:
- Top side: \(9 \, \text{m}\)
- Bottom side: \(9 \, \text{m}\)
- Left side: \(5 \, \text{m} + 5 \, \text{m} = 10 \, \text{m}\)
- Right side: \(5 \, \text{m}\)
- Inner gap: \(2 \, \text{m}\) (not part of the perimeter)
- Perimeter: \(9 + 9 + 10 + 5 = 33 \, \text{m}\)

#### Answers:
- Area: \(60 \, \text{m}^2\)
- Perimeter: \(33 \, \text{m}\)

---

Problem 3:

#### Shape:
- A composite shape consisting of two rectangles:
- Left rectangle: \(8 \, \text{m} \times 5 \, \text{m}\)
- Right rectangle: \(6 \, \text{m} \times 5 \, \text{m}\)

#### Calculations:
1. Area:
- Area of left rectangle: \(8 \, \text{m} \times 5 \, \text{m} = 40 \, \text{m}^2\)
- Area of right rectangle: \(6 \, \text{m} \times 5 \, \text{m} = 30 \, \text{m}^2\)
- Total area: \(40 \, \text{m}^2 + 30 \, \text{m}^2 = 70 \, \text{m}^2\)

2. Perimeter:
- The shape has the following outer sides:
- Top side: \(8 \, \text{m} + 6 \, \text{m} = 14 \, \text{m}\)
- Bottom side: \(8 \, \text{m} + 6 \, \text{m} = 14 \, \text{m}\)
- Left side: \(5 \, \text{m}\)
- Right side: \(5 \, \text{m}\)
- Inner gap: \(2 \, \text{m}\) (not part of the perimeter)
- Perimeter: \(14 + 14 + 5 + 5 = 38 \, \text{m}\)

#### Answers:
- Area: \(70 \, \text{m}^2\)
- Perimeter: \(38 \, \text{m}\)

---

Problem 4:

#### Shape:
- A composite shape consisting of two rectangles:
- Top rectangle: \(15 \, \text{m} \times 4 \, \text{m}\)
- Bottom rectangle: \(10 \, \text{m} \times 4 \, \text{m}\)

#### Calculations:
1. Area:
- Area of top rectangle: \(15 \, \text{m} \times 4 \, \text{m} = 60 \, \text{m}^2\)
- Area of bottom rectangle: \(10 \, \text{m} \times 4 \, \text{m} = 40 \, \text{m}^2\)
- Total area: \(60 \, \text{m}^2 + 40 \, \text{m}^2 = 100 \, \text{m}^2\)

2. Perimeter:
- The shape has the following outer sides:
- Top side: \(15 \, \text{m}\)
- Bottom side: \(15 \, \text{m}\)
- Left side: \(4 \, \text{m} + 4 \, \text{m} = 8 \, \text{m}\)
- Right side: \(4 \, \text{m}\)
- Inner gap: \(5 \, \text{m}\) (not part of the perimeter)
- Perimeter: \(15 + 15 + 8 + 4 = 42 \, \text{m}\)

#### Answers:
- Area: \(100 \, \text{m}^2\)
- Perimeter: \(42 \, \text{m}\)

---

Problem 5:

#### Shape:
- A composite shape consisting of two rectangles:
- Top rectangle: \(12 \, \text{m} \times 2 \, \text{m}\)
- Bottom rectangle: \(10 \, \text{m} \times 7 \, \text{m}\)

#### Calculations:
1. Area:
- Area of top rectangle: \(12 \, \text{m} \times 2 \, \text{m} = 24 \, \text{m}^2\)
- Area of bottom rectangle: \(10 \, \text{m} \times 7 \, \text{m} = 70 \, \text{m}^2\)
- Total area: \(24 \, \text{m}^2 + 70 \, \text{m}^2 = 94 \, \text{m}^2\)

2. Perimeter:
- The shape has the following outer sides:
- Top side: \(12 \, \text{m}\)
- Bottom side: \(10 \, \text{m}\)
- Left side: \(2 \, \text{m} + 7 \, \text{m} = 9 \, \text{m}\)
- Right side: \(2 \, \text{m} + 7 \, \text{m} = 9 \, \text{m}\)
- Inner gap: \(2 \, \text{m}\) (not part of the perimeter)
- Perimeter: \(12 + 10 + 9 + 9 = 40 \, \text{m}\)

#### Answers:
- Area: \(94 \, \text{m}^2\)
- Perimeter: \(40 \, \text{m}\)

---

Problem 6:

#### Shape:
- A composite shape consisting of two rectangles:
- Top rectangle: \(16 \, \text{m} \times 8 \, \text{m}\)
- Bottom rectangle: \(16 \, \text{m} \times 4 \, \text{m}\)

#### Calculations:
1. Area:
- Area of top rectangle: \(16 \, \text{m} \times 8 \, \text{m} = 128 \, \text{m}^2\)
- Area of bottom rectangle: \(16 \, \text{m} \times 4 \, \text{m} = 64 \, \text{m}^2\)
- Total area: \(128 \, \text{m}^2 + 64 \, \text{m}^2 = 192 \, \text{m}^2\)

2. Perimeter:
- The shape has the following outer sides:
- Top side: \(16 \, \text{m}\)
- Bottom side: \(16 \, \text{m}\)
- Left side: \(8 \, \text{m} + 4 \, \text{m} = 12 \, \text{m}\)
- Right side: \(8 \, \text{m} + 4 \, \text{m} = 12 \, \text{m}\)
- Inner gap: \(2 \, \text{m}\) (not part of the perimeter)
- Perimeter: \(16 + 16 + 12 + 12 = 56 \, \text{m}\)

#### Answers:
- Area: \(192 \, \text{m}^2\)
- Perimeter: \(56 \, \text{m}\)

---

Final Answers:

1. Area: \(100 \, \text{m}^2\), Perimeter: \(40 \, \text{m}\)
2. Area: \(60 \, \text{m}^2\), Perimeter: \(33 \, \text{m}\)
3. Area: \(70 \, \text{m}^2\), Perimeter: \(38 \, \text{m}\)
4. Area: \(100 \, \text{m}^2\), Perimeter: \(42 \, \text{m}\)
5. Area: \(94 \, \text{m}^2\), Perimeter: \(40 \, \text{m}\)
6. Area: \(192 \, \text{m}^2\), Perimeter: \(56 \, \text{m}\)

\[
\boxed{
\begin{array}{ll}
1. & \text{Area: } 100 \, \text{m}^2, \text{ Perimeter: } 40 \, \text{m} \\
2. & \text{Area: } 60 \, \text{m}^2, \text{ Perimeter: } 33 \, \text{m} \\
3. & \text{Area: } 70 \, \text{m}^2, \text{ Perimeter: } 38 \, \text{m} \\
4. & \text{Area: } 100 \, \text{m}^2, \text{ Perimeter: } 42 \, \text{m} \\
5. & \text{Area: } 94 \, \text{m}^2, \text{ Perimeter: } 40 \, \text{m} \\
6. & \text{Area: } 192 \, \text{m}^2, \text{ Perimeter: } 56 \, \text{m} \\
\end{array}
}
\]