Area and perimeter worksheet with six geometric shapes and space to solve equations.

To solve the problems involving area and perimeter for the given shapes, we will use the following formulas:

Formulas:

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

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

---

Step-by-Step Solutions:

#### 1. Rectangle (11m × 12m)
- Area:
\[
\text{Area} = \text{Length} \times \text{Width} = 11 \, \text{m} \times 12 \, \text{m} = 132 \, \text{m}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 2 \times (11 \, \text{m} + 12 \, \text{m}) = 2 \times 23 \, \text{m} = 46 \, \text{m}
\]

#### 2. Rectangle (4m × 12m)
- Area:
\[
\text{Area} = \text{Length} \times \text{Width} = 4 \, \text{m} \times 12 \, \text{m} = 48 \, \text{m}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 2 \times (4 \, \text{m} + 12 \, \text{m}) = 2 \times 16 \, \text{m} = 32 \, \text{m}
\]

#### 3. Triangle (Base = 3m, Height = 12m)
- Area:
\[
\text{Area} = 0.5 \times \text{Base} \times \text{Height} = 0.5 \times 3 \, \text{m} \times 12 \, \text{m} = 0.5 \times 36 \, \text{m}^2 = 18 \, \text{m}^2
\]

#### 4. Rectangle (7m × 3m)
- Area:
\[
\text{Area} = \text{Length} \times \text{Width} = 7 \, \text{m} \times 3 \, \text{m} = 21 \, \text{m}^2
\]
- Perimeter:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 2 \times (7 \, \text{m} + 3 \, \text{m}) = 2 \times 10 \, \text{m} = 20 \, \text{m}
\]

#### 5. Triangle (Base = 4m, Height = 11m)
- Area:
\[
\text{Area} = 0.5 \times \text{Base} \times \text{Height} = 0.5 \times 4 \, \text{m} \times 11 \, \text{m} = 0.5 \times 44 \, \text{m}^2 = 22 \, \text{m}^2
\]

#### 6. Square (12m × 12m)
- Area:
\[
\text{Area} = \text{Side} \times \text{Side} = 12 \, \text{m} \times 12 \, \text{m} = 144 \, \text{m}^2
\]
- Perimeter:
\[
\text{Perimeter} = 4 \times \text{Side} = 4 \times 12 \, \text{m} = 48 \, \text{m}
\]

---

Final Answers:

1. Rectangle (11m × 12m):
- Area: \( \boxed{132} \, \text{m}^2 \)
- Perimeter: \( \boxed{46} \, \text{m} \)

2. Rectangle (4m × 12m):
- Area: \( \boxed{48} \, \text{m}^2 \)
- Perimeter: \( \boxed{32} \, \text{m} \)

3. Triangle (Base = 3m, Height = 12m):
- Area: \( \boxed{18} \, \text{m}^2 \)

4. Rectangle (7m × 3m):
- Area: \( \boxed{21} \, \text{m}^2 \)
- Perimeter: \( \boxed{20} \, \text{m} \)

5. Triangle (Base = 4m, Height = 11m):
- Area: \( \boxed{22} \, \text{m}^2 \)

6. Square (12m × 12m):
- Area: \( \boxed{144} \, \text{m}^2 \)
- Perimeter: \( \boxed{48} \, \text{m} \)

---

Boxed Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & \text{Area: } 132 \, \text{m}^2, \text{ Perimeter: } 46 \, \text{m} \\
2. & \text{Area: } 48 \, \text{m}^2, \text{ Perimeter: } 32 \, \text{m} \\
3. & \text{Area: } 18 \, \text{m}^2 \\
4. & \text{Area: } 21 \, \text{m}^2, \text{ Perimeter: } 20 \, \text{m} \\
5. & \text{Area: } 22 \, \text{m}^2 \\
6. & \text{Area: } 144 \, \text{m}^2, \text{ Perimeter: } 48 \, \text{m} \\
\end{array}
}
\]