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Let's analyze and solve the questions step by step:

### 18. Which figure is not a polygon?

A **polygon** is a closed figure with straight sides. 
- **Figure A** is a polygon (a convex pentagon).
- **Figure B** appears to have curves or non-straight edges, which makes it not a polygon.
- **Figure C** is a rectangle, which is a polygon.
- **Figure D** seems to have part of a circle (a curved edge), so it is also not a polygon.

Thus, the correct answer is **B. Figure B**.

### 19. Find the perimeter of the convex pentagon (Figure A).

The perimeter of a shape is the sum of the lengths of all its sides. For **Figure A**, the sides are given as 25 cm, 15 cm, 12 cm, 12 cm, and 15 cm.

\[
\text{Perimeter} = 25 + 15 + 12 + 12 + 15 = 79 \text{ cm}
\]

None of the given answer choices match this exactly, so let's verify this by checking the original intention of the question, but based on the numbers provided, the perimeter is **79 cm**, not any of the listed options.

### 20. Suppose the length and width of the rectangle (Figure C) are doubled. What is its perimeter?

The original dimensions of **Figure C** are 15 cm by 8 cm. The perimeter of a rectangle is calculated as:

\[
\text{Perimeter} = 2(\text{Length} + \text{Width})
\]

First, let's find the current perimeter:

\[
\text{Perimeter} = 2(15 + 8) = 2(23) = 46 \text{ cm}
\]

Now, if both the length and width are doubled (new dimensions: 30 cm and 16 cm), the new perimeter would be:

\[
\text{New Perimeter} = 2(30 + 16) = 2(46) = 92 \text{ cm}
\]

So the correct answer is **B. 92 cm**.

### Bonus: Each side of a square is \( 2x - 6 \) yards long. If the perimeter of the square is 72 yards, what is the value of \( x \)?

The perimeter of a square is \( 4 \times \text{side length} \). Here, each side length is given as \( 2x - 6 \). So, we set up the equation for the perimeter:

\[
4(2x - 6) = 72
\]

First, simplify the left side:

\[
8x - 24 = 72
\]

Add 24 to both sides:

\[
8x = 96
\]

Now, divide by 8:

\[
x = 12
\]

Thus, the value of \( x \) is **12**.

---

Do you need further clarification or details on any part? Here are some additional related questions:

1. What defines a polygon?
2. How can you determine whether a figure is convex or concave?
3. What would be the perimeter if the rectangle's length was tripled instead of doubled?
4. How can the formula for the perimeter of a rectangle be derived?
5. What happens to the area of the rectangle if its dimensions are doubled?

**Tip:** Always check whether a shape has curved sides when determining if it is a polygon!

Which figure is not a polygon? Find the perimeter of the convex pentagon. Suppose the length and width of the rectangle are doubled. What is its perimeter? Bonus: Each side of a square is 2x - 6 yards long. If the perimeter of the square is 72 yards, what is the value of x?

Learn to identify polygons, calculate the perimeter of a convex pentagon, and solve algebraic equations for square side lengths. This exercise is designed for Grades 6-8 and covers geometry, perimeter formulas, and algebraic problem-solving.

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