https://file.aiquickdraw.com/mathbot/file/17248807750141stlh9nf.jpg

To find the perimeter and area of the shapes shown in the image, let's analyze each shape separately.

The image contains a trapezoid on the left (green) and a rectangle on the right (blue). Here's how we can calculate their areas and perimeters:

### 1. **Trapezoid (Green)**

**Vertices Coordinates**:
- Top-left: \((-4, 4)\)
- Bottom-left: \((-4, 0)\)
- Bottom-right: \((0, 0)\)
- Top-right: \((0, 4)\)

**Area Calculation**:
- Base 1 (vertical line segment from \((-4, 4)\) to \((-4, 0)\)): 4 units
- Base 2 (vertical line segment from \((0, 4)\) to \((0, 0)\)): 4 units
- Height (distance between the bases): 4 units

Using the trapezoid area formula:
\[
\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}
\]
\[
\text{Area} = \frac{1}{2} \times (4 + 4) \times 4 = 16 \, \text{square units}
\]

**Perimeter Calculation**:
- Sum of all sides: \(4 + 4 + 4 + 4 = 16\) units

### 2. **Rectangle (Blue)**

**Vertices Coordinates**:
- Bottom-left: \((0, 0)\)
- Top-left: \((0, 4)\)
- Top-right: \((2, 4)\)
- Bottom-right: \((2, 0)\)

**Area Calculation**:
- Length: 2 units (distance from \((0, 0)\) to \((2, 0)\))
- Width: 4 units (distance from \((0, 0)\) to \((0, 4)\))

Using the rectangle area formula:
\[
\text{Area} = \text{Length} \times \text{Width} = 2 \times 4 = 8 \, \text{square units}
\]

**Perimeter Calculation**:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 2 \times (2 + 4) = 12 \, \text{units}
\]

### Combined Results:
- **Total Area**: \(16 + 8 = 24 \, \text{square units}\)
- **Total Perimeter**: This depends if both shapes are counted together, if we subtract the common side between them:
  - For the combined perimeter: \(16 + 12 - 4 = 24 \, \text{units}\) (subtract the shared side \((0, 0)\) to \((0, 4)\))

Would you like more details on any step, or do you have any other questions?

### Follow-up Questions:
1. How would the calculations change if the shapes were on a different coordinate system?
2. What is the perimeter and area of a trapezoid with different bases and height?
3. Can you calculate the perimeter and area of a circle inscribed inside the rectangle?
4. What formula would you use to find the diagonal length of the rectangle?
5. How do you determine the perimeter of a shape if it has an irregular form?

**Tip:** Always check for shared sides when calculating the perimeter of combined shapes to avoid double-counting lengths!

Learn how to calculate the perimeter and area of a trapezoid and a rectangle using coordinate geometry and basic geometric formulas. This detailed solution covers the calculation steps, including formulas for area and perimeter. Suitable for high school students studying geometry.

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