https://file.aiquickdraw.com/mathbot/file/172670573399690fqrspv.jpg

Let's analyze the given figure and solve the problem based on the information provided.

### 1. Original Shape Measurements:
The original polygon appears to be made up of smaller square units. Each square has an area of \(1 \text{ unit}^2\) (since one side is 1 unit). The shape looks like an "L" with the following composition:
- The height consists of 3 squares vertically.
- The base consists of 2 squares horizontally, forming the bottom of the "L."

#### Total Area of Original Polygon:
The number of squares forming the polygon is:
- 3 vertical squares + 2 horizontal squares (including the bottom one that overlaps) = **5 square units**.

Thus, the **area of the original polygon** is:
\[
\text{Area of original polygon} = 5 \text{ units}^2
\]

#### Perimeter of Original Polygon:
To find the perimeter, count the exposed sides of the squares:
- Each small square has sides of 1 unit.
- The vertical sides: 3 units on the left, plus 2 vertical units from the bottom.
- The horizontal sides: 2 units on the top (across two squares), plus 1 unit at the bottom.

Thus, the **perimeter of the original polygon** is:
\[
\text{Perimeter of original polygon} = 3 + 2 + 2 + 1 + 1 + 1 = 10 \text{ units}
\]

### 2. Scaled Shape (Scale Factor = 2):
A scale factor of 2 means each side of the polygon will be doubled, and the new area will increase by the square of the scale factor.

#### Area of the Scaled Polygon:
The area of the scaled polygon will be:
\[
\text{Area of scaled polygon} = 5 \times (2^2) = 5 \times 4 = 20 \text{ units}^2
\]

#### Perimeter of the Scaled Polygon:
Since each side is doubled, the perimeter will also be doubled:
\[
\text{Perimeter of scaled polygon} = 10 \times 2 = 20 \text{ units}
\]

### Final Answer:
- **Area of the scaled polygon:** 20 square units
- **Perimeter of the scaled polygon:** 20 units

Would you like more details on any part of the solution? Here are some related questions to consider:

1. What would happen to the area if the scale factor was 3?
2. How do we calculate the perimeter of more complex polygons?
3. Why does the area increase by the square of the scale factor?
4. How does the perimeter change with different scale factors?
5. What is the relationship between scale factors and transformations in geometry?

**Tip:** When scaling a polygon, remember that the area changes by the square of the scale factor, while the perimeter changes linearly.

Imagine a scaled copy of the figure that has a scale factor of 2. What are the area and perimeter of the scaled copy?

Learn how to calculate the area and perimeter of a polygon after scaling by a factor of 2. Understand key geometry concepts including scaling, area, and perimeter calculations. Suitable for Grades 6-8.

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