Classifying Regular or Irregular Polygons

A polygon has all sides and angles equal. Which of the following best describes this polygon?

• Regular and Convex

• Regular and Non-Convex

• Irregular and Convex

• Irregular and Non-Convex

Answer explanation

A polygon with all sides and angles equal is described as Regular and Convex.

A hexagon has one interior angle greater than 180 degrees. How would you classify this polygon?

• Regular and Convex

• Regular and Non-Convex

• Irregular and Convex

• Irregular and Non-Convex

Answer explanation

A hexagon with one interior angle greater than 180 degrees is irregular (not all sides or angles are equal) and non-convex (at least one interior angle is greater than 180 degrees). Therefore, the correct classification is Irregular and Non-Convex.

Which of the following polygons is both convex and regular?

• A hexagon with one angle measuring 200 degrees

• An equilateral triangle

• A star-shaped polygon

• A pentagon with unequal side lengths

Answer explanation

An equilateral triangle is both convex (all interior angles are less than 180 degrees) and regular (all sides and angles are equal).

Consider a pentagon with no two sides equal and all interior angles less than 180 degrees. Which classification fits this polygon?

• Regular and Convex

• Regular and Non-Convex

• Irregular and Convex

• Irregular and Non-Convex

Answer explanation

The correct classification for the pentagon described is Irregular and Convex because it has unequal sides and all interior angles are less than 180 degrees.

A star-shaped polygon is given. How should it be classified?

• Regular and Convex

• Regular and Non-Convex

• Irregular and Convex

• Irregular and Non-Convex

Answer explanation

The star-shaped polygon does not have equal sides and angles, making it irregular. Additionally, it has at least one inward angle, making it non-convex.

A polygon has unequal side lengths and one interior angle measuring 210 degrees. How would you classify this polygon?

• Regular and Convex

• Regular and Non-Convex

• Irregular and Convex

• Irregular and Non-Convex

Answer explanation

The polygon is irregular because it has unequal side lengths and non-convex because it has an interior angle measuring 210 degrees. Therefore, the correct classification is Irregular and Non-Convex.

An octagon has all sides of equal length but varying interior angles. What is the best classification for this polygon?

• Regular and Convex

• Regular and Non-Convex

• Irregular and Convex

• Irregular and Non-Convex

Answer explanation

The best classification for an octagon with all sides of equal length but varying interior angles is Regular and Non-Convex, as it has equal sides but not all interior angles are equal.

A polygon has sides of different lengths and all interior angles equal to 135 degrees. How should it be classified?

Answer explanation

The polygon should be classified as a concave polygon since all interior angles are equal to 135 degrees.

Consider a polygon with some vertices pointing inward and some pointing outward, with interior angles both less than and greater than 180 degrees. What is its classification?

• Regular and Convex

• Regular and Non-Convex

• Irregular and Convex

• Irregular and Non-Convex

Answer explanation

The correct classification for a polygon with vertices pointing inward and outward, with interior angles both less than and greater than 180 degrees, is Irregular and Non-Convex.

A decagon has each angle equal to 144 degrees and all sides are equal. How would you classify this polygon?

• Regular and Convex

• Regular and Non-Convex

• Irregular and Convex

• Irregular and Non-Convex

Answer explanation

The decagon has equal angles and sides, making it regular. Since all interior angles are less than 180 degrees, it is convex.