Math worksheet for identifying and calculating missing side lengths in similar polygons.

The task in the image involves identifying and naming polygons based on their shapes. Polygons are closed, two-dimensional shapes with straight sides. The goal is to match each shape with its correct name from a list of polygon names provided.

Step-by-Step Solution:

1. Identify the Shapes:
- Carefully observe each shape in the image.
- Determine the number of sides and angles for each shape.

2. Match the Shapes with Polygon Names:
- Use the list of polygon names provided (e.g., triangle, quadrilateral, pentagon, hexagon, etc.) to identify the correct name for each shape.

3. Write the Answers:
- Write the name of the polygon next to each shape.

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Detailed Analysis of Each Shape:

#### Shape 1:
- Description: A three-sided figure.
- Identification: This is a triangle.
- Answer: Triangle

#### Shape 2:
- Description: A four-sided figure with one pair of parallel sides.
- Identification: This is a trapezoid.
- Answer: Trapezoid

#### Shape 3:
- Description: A five-sided figure.
- Identification: This is a pentagon.
- Answer: Pentagon

#### Shape 4:
- Description: A six-sided figure.
- Identification: This is a hexagon.
- Answer: Hexagon

#### Shape 5:
- Description: A four-sided figure with opposite sides parallel.
- Identification: This is a parallelogram.
- Answer: Parallelogram

#### Shape 6:
- Description: A four-sided figure with all sides equal and all angles equal.
- Identification: This is a square.
- Answer: Square

#### Shape 7:
- Description: A four-sided figure with one pair of parallel sides.
- Identification: This is a trapezoid.
- Answer: Trapezoid

#### Shape 8:
- Description: A seven-sided figure.
- Identification: This is a heptagon.
- Answer: Heptagon

#### Shape 9:
- Description: An eight-sided figure.
- Identification: This is an octagon.
- Answer: Octagon

#### Shape 10:
- Description: A four-sided figure with one pair of parallel sides.
- Identification: This is a trapezoid.
- Answer: Trapezoid

#### Shape 11:
- Description: A four-sided figure with opposite sides parallel.
- Identification: This is a rectangle.
- Answer: Rectangle

#### Shape 12:
- Description: A four-sided figure with one pair of parallel sides.
- Identification: This is a trapezoid.
- Answer: Trapezoid

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Final Answers:

1. Triangle
2. Trapezoid
3. Pentagon
4. Hexagon
5. Parallelogram
6. Square
7. Trapezoid
8. Heptagon
9. Octagon
10. Trapezoid
11. Rectangle
12. Trapezoid

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Boxed Final Answer:

\[
\boxed{
\text{Triangle, Trapezoid, Pentagon, Hexagon, Parallelogram, Square, Trapezoid, Heptagon, Octagon, Trapezoid, Rectangle, Trapezoid}
}
\]