Area and Perimeter worksheet with six geometry problems to solve.

To solve the problems related to area and perimeter for each shape, we will use the following formulas:

Formulas:

1. Rectangle:
- Area = Length × Width
- Perimeter = 2 × (Length + Width)

2. Triangle:
- Area = 0.5 × Base × Height

3. Square:
- Area = Side × Side
- Perimeter = 4 × Side

---

Solutions:

#### 1. Rectangle (10m × 4m)
- Area:
\[
\text{Area} = \text{Length} \times \text{Width} = 10 \, \text{m} \times 4 \, \text{m} = 40 \, \text{m}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 2 \times (10 \, \text{m} + 4 \, \text{m}) = 2 \times 14 \, \text{m} = 28 \, \text{m}
\]

#### 2. Triangle (Base = 9m, Height = 6m)
- Area:
\[
\text{Area} = 0.5 \times \text{Base} \times \text{Height} = 0.5 \times 9 \, \text{m} \times 6 \, \text{m} = 0.5 \times 54 \, \text{m}^2 = 27 \, \text{m}^2
\]

#### 3. Square (Side = 7m)
- Area:
\[
\text{Area} = \text{Side} \times \text{Side} = 7 \, \text{m} \times 7 \, \text{m} = 49 \, \text{m}^2
\]
- Perimeter:
\[
\text{Perimeter} = 4 \times \text{Side} = 4 \times 7 \, \text{m} = 28 \, \text{m}
\]

#### 4. Triangle (Base = 8m, Height = 12m)
- Area:
\[
\text{Area} = 0.5 \times \text{Base} \times \text{Height} = 0.5 \times 8 \, \text{m} \times 12 \, \text{m} = 0.5 \times 96 \, \text{m}^2 = 48 \, \text{m}^2
\]

#### 5. Rectangle (20m × 7m)
- Area:
\[
\text{Area} = \text{Length} \times \text{Width} = 20 \, \text{m} \times 7 \, \text{m} = 140 \, \text{m}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 2 \times (20 \, \text{m} + 7 \, \text{m}) = 2 \times 27 \, \text{m} = 54 \, \text{m}
\]

#### 6. Rectangle (11m × 8m)
- Area:
\[
\text{Area} = \text{Length} \times \text{Width} = 11 \, \text{m} \times 8 \, \text{m} = 88 \, \text{m}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 2 \times (11 \, \text{m} + 8 \, \text{m}) = 2 \times 19 \, \text{m} = 38 \, \text{m}
\]

---

Final Answers:

1. Rectangle (10m × 4m):
- Area: \( \boxed{40 \, \text{m}^2} \)
- Perimeter: \( \boxed{28 \, \text{m}} \)

2. Triangle (Base = 9m, Height = 6m):
- Area: \( \boxed{27 \, \text{m}^2} \)

3. Square (Side = 7m):
- Area: \( \boxed{49 \, \text{m}^2} \)
- Perimeter: \( \boxed{28 \, \text{m}} \)

4. Triangle (Base = 8m, Height = 12m):
- Area: \( \boxed{48 \, \text{m}^2} \)

5. Rectangle (20m × 7m):
- Area: \( \boxed{140 \, \text{m}^2} \)
- Perimeter: \( \boxed{54 \, \text{m}} \)

6. Rectangle (11m × 8m):
- Area: \( \boxed{88 \, \text{m}^2} \)
- Perimeter: \( \boxed{38 \, \text{m}} \)

---

Boxed Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & \text{Area: } 40 \, \text{m}^2, \text{ Perimeter: } 28 \, \text{m} \\
2. & \text{Area: } 27 \, \text{m}^2 \\
3. & \text{Area: } 49 \, \text{m}^2, \text{ Perimeter: } 28 \, \text{m} \\
4. & \text{Area: } 48 \, \text{m}^2 \\
5. & \text{Area: } 140 \, \text{m}^2, \text{ Perimeter: } 54 \, \text{m} \\
6. & \text{Area: } 88 \, \text{m}^2, \text{ Perimeter: } 38 \, \text{m} \\
\end{array}
}
\]