https://file.aiquickdraw.com/mathbot/file/17292795431213cbf8yt3.jpg

To solve this problem, let's go step by step.

### Step 1: Apply the Zoom Factor of 2
When a geometric shape is **enlarged by a zoom factor of 2**, each of its side lengths is **multiplied by 2**. 

The original side lengths are:
- 4, 3, 6, and 5.

After applying the zoom factor of 2:
- \(4 \times 2 = 8\)
- \(3 \times 2 = 6\)
- \(6 \times 2 = 12\)
- \(5 \times 2 = 10\)

### Step 2: Calculate the Perimeter of the New Figure
The **perimeter** is the sum of all side lengths.

\[
\text{Perimeter} = 8 + 6 + 12 + 10 = 36
\]

Thus, the **perimeter of the new figure is 36 units**.

### Step 3: Calculate the Area of the New Figure
The shape resembles a **trapezoid**, with two parallel sides (3 and 6 originally) and height 4.

#### Original Area of the Trapezoid:
Using the formula for the area of a trapezoid:

\[
\text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h
\]

Where:
- \(b_1 = 3\)
- \(b_2 = 6\)
- \(h = 4\)

\[
\text{Area} = \frac{1}{2} \times (3 + 6) \times 4 = \frac{1}{2} \times 9 \times 4 = 18 \, \text{square units}
\]

#### Area of the Enlarged Figure:
Since the enlargement factor is 2, the area will increase by \(2^2 = 4\) times.

\[
\text{New Area} = 18 \times 4 = 72 \, \text{square units}
\]

### Final Answers:
- **Perimeter of the new figure:** 36 units.
- **Area of the new figure:** 72 square units.

---

Do you need any further details or have any questions?  
Here are some follow-up questions you might find helpful:

1. How does the area scale with different zoom factors?
2. How would the perimeter change with a zoom factor of 3 instead?
3. What if the shape was rotated—would the perimeter or area change?
4. Can you confirm if all shapes scale similarly with zoom factors?
5. How would we calculate the side lengths if the original diagram had missing measurements?

**Tip:** Remember that **area** scales with the square of the zoom factor, while **perimeter** scales linearly!

Enlarge the following geometric shape by a zoom factor of 2. What is the perimeter of the new figure? What is the area of the new figure?

Learn how to enlarge a geometric shape by a zoom factor of 2 and calculate the perimeter and area of the new figure. This problem covers key geometry concepts, including scaling, perimeter, and area calculations, with a focus on trapezoidal shapes. Suitable for students in Grades 6-8.

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