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!