Which Of The Following Figures Is Not A Polygon

##Which of the Following Figures Is Not a Polygon?

Understanding what makes a shape a polygon is essential for geometry, design, and everyday problem‑solving. When you encounter a set of figures and are asked which of the following figures is not a polygon, you need a clear set of criteria to evaluate each option. This article walks you through the definition of a polygon, the properties that distinguish polygons from other shapes, and a practical, step‑by‑method you can apply to any collection of figures. By the end, you’ll be able to spot non‑polygons quickly and confidently.

What Is a Polygon?

A polygon is a two‑dimensional geometric figure that satisfies three fundamental conditions:

1. Closed shape – The figure’s boundary forms a complete loop with no gaps.
2. Straight sides – Every segment of the boundary is a straight line segment; curves are not allowed.
3. Finite number of sides – The shape has at least three sides, and the number of sides is a whole number (3, 4, 5, …).

If any of these conditions fails, the figure is not a polygon.

Examples:

• A triangle (3 straight sides, closed) ✔️
• A square (4 straight sides, closed) ✔️
• A pentagon (5 straight sides, closed) ✔️

Non‑examples:

• A circle (curved boundary) ❌
• An open “U” shape (not closed) ❌
• A shape with a mix of straight and curved edges (e.g., a semi‑circle) ❌

Core Characteristics to Check

When evaluating a figure, run through this quick checklist. If the answer is “no” to any item, the figure is not a polygon.

If the figure passes the first three rows, it is a polygon (simple or complex depending on self‑intersection). ---

Common Types of Polygons

Knowing the families of polygons helps you recognize them instantly.

• Triangles – 3 sides (equilateral, isosceles, scalene).
• Quadrilaterals – 4 sides (square, rectangle, rhombus, trapezoid, kite).
• Pentagons – 5 sides (regular or irregular). - Hexagons – 6 sides (often seen in honeycomb patterns). - Heptagons, Octagons, … – 7, 8, … sides respectively.
• Regular polygons – All sides and angles equal (e.g., regular hexagon).
• Irregular polygons – Sides and/or angles differ (e.g., a scalene quadrilateral).

All of these share the closed, straight‑sided definition.

Typical Non‑Polygon Figures

When a test asks which of the following figures is not a polygon, the distractors usually belong to one of these categories:

1. Curved‑boundary shapes – circles, ellipses, ovals, parabolas, arcs.
2. Open shapes – line segments, rays, “C” shapes, zigzags that do not loop back.
3. Mixed‑boundary shapes – figures that combine straight lines with curves (e.g., a shape with a straight base and a semicircular top).
4. Point or dot – zero‑dimensional; no sides at all.
5. Fractal or infinitely detailed boundaries – while mathematically interesting, they fail the “finite number of straight sides” rule in elementary geometry.

Recognizing these patterns lets you eliminate options quickly.

Step‑by‑Step Guide to Identify the Non‑Polygon Follow this procedure whenever you face a multiple‑choice question about polygons.

1. Inspect each figure for closure

   • Imagine drawing the shape without lifting your pen. If you end up at a different point or leave a gap, discard it.

2. Examine the boundary for curves

   • Run your eye along the edge. Any smooth bend, arc, or wavy line means the figure fails the straight‑sides rule.

3. Count the straight line segments

   • Tally each distinct straight side. If the total is less than three, the figure cannot be a polygon.

4. Check for self‑intersection (if the definition you’re using excludes it)

   • Some textbooks consider a self‑intersecting shape (like a star polygon) still a polygon, while others call it a “complex polygon.” Know which convention your source follows.

5. Select the figure that fails any of the above

   • The one that does not meet all criteria is the answer to which of the following figures is not a polygon.

Example Walkthrough
Suppose you see four options:

• A. A regular hexagon
• B. A shape that looks like a “D” (straight vertical line on the left, a semicircle on the right)
• C. A scalene triangle
• D. A rectangle with a small notch cut out (still straight edges)

Apply the steps:

• A is closed, all sides straight, six sides → polygon.
• B is closed, but the right side is a curve → not a polygon.
• C is closed, three straight sides → polygon. - D is closed, all edges straight (the notch adds extra sides) → polygon.

Thus, the correct answer is B.

Frequently Asked Questions

Q1: Can a polygon have curved sides if they are very short?

A: No. By definition, a polygon’s sides must be straight line segments, regardless of length. Any curvature, however minor, disqualifies the figure.

Q2: Are shapes like a

star polygon polygons? A: This depends on the definition being used. Traditionally, polygons are defined as having a finite number of straight sides. A star polygon, with its intersecting lines, doesn’t fit this strict definition. However, some modern definitions broaden the concept to include “complex polygons” that may have self-intersecting boundaries. Always check the question’s wording and the textbook’s definition to determine the correct answer.

Q3: What about shapes with holes?

A: A shape with a hole is still considered a polygon if the outer boundary consists of straight line segments and has at least three sides. The hole itself doesn’t affect the classification as long as the overall figure adheres to the fundamental requirements of a polygon.

Q4: How do I differentiate between a complex polygon and a non-polygon?

A: A complex polygon, like a star, has intersecting sides. A non-polygon, on the other hand, will always have a gap or an incomplete boundary, or contain curves. The key is to look for a figure that doesn’t close completely and doesn’t consist solely of straight lines.

Conclusion

Identifying non-polygons can seem tricky at first, but by systematically applying the outlined steps – assessing closure, scrutinizing for curves, counting straight sides, and understanding the specific definition being used – you can confidently tackle these types of questions. Remember that the core principle remains: a polygon must be a closed shape formed entirely by straight line segments. Practice with various examples, paying close attention to the nuances of each shape, and you’ll quickly develop a keen eye for recognizing these geometric figures. Mastering this skill will not only improve your performance on standardized tests but also enhance your overall understanding of fundamental geometric concepts.