Name the following polygons worksheet with various geometric shapes.

Let's solve the problem step by step.

The task is to name the following polygons based on their shape and number of sides. Each polygon is a closed figure made up of straight line segments. We identify them by counting the number of sides and using standard names for polygons.

Here are the 12 shapes in the image, arranged in 4 rows of 3:

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Row 1:

1. First shape (top-left):
- It has 4 sides, with one pair of parallel sides (the top and bottom).
- This is a trapezoid (specifically, a trapezium in some regions).

2. Second shape:
- Also has 4 sides, but no sides appear parallel? Wait — actually, it looks like a parallelogram (opposite sides are parallel and equal), but skewed.
- So this is a parallelogram.

3. Third shape:
- Has 3 sides → Triangle

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Row 2:

4. Fourth shape:
- 4 sides, opposite sides are parallel and equal, but angles are not right angles → Parallelogram (again, similar to #2)

5. Fifth shape:
- 6 sides → Hexagon

6. Sixth shape:
- 4 sides, with two pairs of parallel sides, and appears to have right angles → Rectangle

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Row 3:

7. Seventh shape:
- 5 sides → Pentagon

8. Eighth shape:
- 4 sides, appears to be a rectangle rotated → Rectangle

9. Ninth shape:
- 5 sides, but shaped like an "arrowhead" or "house roof" → Still Pentagon (a concave pentagon)

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Row 4:

10. Tenth shape:
- 8 sides → Octagon

11. Eleventh shape:
- 4 sides, all equal and right angles → Square

12. Twelfth shape:
- 6 sides, but irregular and concave → Hexagon (a concave hexagon)

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✔ Final Answers:

Label each blank below the shapes:

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

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🔍 Explanation:

- Polygons are named based on the number of sides:
- 3 sides → Triangle
- 4 sides → Quadrilateral (subtypes: square, rectangle, rhombus, parallelogram, trapezoid)
- 5 sides → Pentagon
- 6 sides → Hexagon
- 8 sides → Octagon
- Shapes with parallel sides or equal angles/sides get more specific names.
- Concave vs convex doesn't change the name — just the classification.

✔ So, fill in the blanks as follows:

```
Trapezoid Parallelogram Triangle
Parallelogram Hexagon Rectangle
Pentagon Rectangle Pentagon
Octagon Square Hexagon
```

Let me know if you'd like this formatted as a printable answer key!