Answer key showing formulas and solutions for finding perimeter and area of parallelograms, triangles, and trapezoids.

The image you provided contains a worksheet with problems related to the perimeter and area of parallelograms, triangles, trapezoids, and other geometric shapes. Below, I will explain the solutions for each problem step by step.

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Problem 1:

Shape: Parallelogram
Given: Base = 7 cm, Height = 8 cm
Task: Find the perimeter and area.

#### Solution:
1. Perimeter of a Parallelogram:
- Formula: \( P = 2 \times (\text{Base} + \text{Side}) \)
- Here, the base is 7 cm, but the side length is not given. Assuming the side is also 7 cm (as it is a square-like figure in the diagram):
\[
P = 2 \times (7 + 7) = 2 \times 14 = 28 \, \text{cm}
\]

2. Area of a Parallelogram:
- Formula: \( A = \text{Base} \times \text{Height} \)
- Given: Base = 7 cm, Height = 8 cm
\[
A = 7 \times 8 = 56 \, \text{cm}^2
\]

Answer:
\[
P = 28 \, \text{cm}, \quad A = 56 \, \text{cm}^2
\]

---

Problem 2:

Shape: Triangle
Given: Base = 3.2 ft, Height = 2.9 ft
Task: Find the area.

#### Solution:
1. Area of a Triangle:
- Formula: \( A = \frac{1}{2} \times \text{Base} \times \text{Height} \)
- Given: Base = 3.2 ft, Height = 2.9 ft
\[
A = \frac{1}{2} \times 3.2 \times 2.9 = \frac{1}{2} \times 9.28 = 4.64 \, \text{ft}^2
\]

Answer:
\[
A = 4.64 \, \text{ft}^2
\]

---

Problem 3:

Shape: Trapezoid
Given: Bases = 1.2 m and 3.0 m, Height = 1.5 m
Task: Find the area.

#### Solution:
1. Area of a Trapezoid:
- Formula: \( A = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} \)
- Given: Base₁ = 1.2 m, Base₂ = 3.0 m, Height = 1.5 m
\[
A = \frac{1}{2} \times (1.2 + 3.0) \times 1.5 = \frac{1}{2} \times 4.2 \times 1.5 = \frac{1}{2} \times 6.3 = 3.15 \, \text{m}^2
\]

Answer:
\[
A = 3.15 \, \text{m}^2
\]

---

Problem 4:

Shape: Rectangle
Given: Length = 13 mm, Width = 24 mm
Task: Find the perimeter and area.

#### Solution:
1. Perimeter of a Rectangle:
- Formula: \( P = 2 \times (\text{Length} + \text{Width}) \)
- Given: Length = 13 mm, Width = 24 mm
\[
P = 2 \times (13 + 24) = 2 \times 37 = 74 \, \text{mm}
\]

2. Area of a Rectangle:
- Formula: \( A = \text{Length} \times \text{Width} \)
- Given: Length = 13 mm, Width = 24 mm
\[
A = 13 \times 24 = 312 \, \text{mm}^2
\]

Answer:
\[
P = 74 \, \text{mm}, \quad A = 312 \, \text{mm}^2
\]

---

Problem 5:

Shape: Trapezoid
Given: Bases = 10 cm and 30 cm, Height = 12 cm
Task: Find the area.

#### Solution:
1. Area of a Trapezoid:
- Formula: \( A = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} \)
- Given: Base₁ = 10 cm, Base₂ = 30 cm, Height = 12 cm
\[
A = \frac{1}{2} \times (10 + 30) \times 12 = \frac{1}{2} \times 40 \times 12 = \frac{1}{2} \times 480 = 240 \, \text{cm}^2
\]

Answer:
\[
A = 240 \, \text{cm}^2
\]

---

Problem 6:

Shape: Triangle
Given: Base = 7.5 cm, Height = 6.7 cm
Task: Find the area.

#### Solution:
1. Area of a Triangle:
- Formula: \( A = \frac{1}{2} \times \text{Base} \times \text{Height} \)
- Given: Base = 7.5 cm, Height = 6.7 cm
\[
A = \frac{1}{2} \times 7.5 \times 6.7 = \frac{1}{2} \times 50.25 = 25.125 \, \text{cm}^2
\]

Answer:
\[
A = 25.125 \, \text{cm}^2
\]

---

Problem 7:

Shape: Trapezoid
Given: Bases = 12 cm and 18 cm, Height = 5 cm
Task: Find the area.

#### Solution:
1. Area of a Trapezoid:
- Formula: \( A = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} \)
- Given: Base₁ = 12 cm, Base₂ = 18 cm, Height = 5 cm
\[
A = \frac{1}{2} \times (12 + 18) \times 5 = \frac{1}{2} \times 30 \times 5 = \frac{1}{2} \times 150 = 75 \, \text{cm}^2
\]

Answer:
\[
A = 75 \, \text{cm}^2
\]

---

Problem 8:

Shape: Triangle
Given: Base = 9 m, Height = 10 m
Task: Find the area.

#### Solution:
1. Area of a Triangle:
- Formula: \( A = \frac{1}{2} \times \text{Base} \times \text{Height} \)
- Given: Base = 9 m, Height = 10 m
\[
A = \frac{1}{2} \times 9 \times 10 = \frac{1}{2} \times 90 = 45 \, \text{m}^2
\]

Answer:
\[
A = 45 \, \text{m}^2
\]

---

Final Answer:

\[
\boxed{
\begin{aligned}
1. & \, P = 28 \, \text{cm}, \, A = 56 \, \text{cm}^2 \\
2. & \, A = 4.64 \, \text{ft}^2 \\
3. & \, A = 3.15 \, \text{m}^2 \\
4. & \, P = 74 \, \text{mm}, \, A = 312 \, \text{mm}^2 \\
5. & \, A = 240 \, \text{cm}^2 \\
6. & \, A = 25.125 \, \text{cm}^2 \\
7. & \, A = 75 \, \text{cm}^2 \\
8. & \, A = 45 \, \text{m}^2 \\
\end{aligned}
}
\]