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Quizzes > High School Quizzes > Mathematics

Practice Quiz: Which Figure Isn't a Polygon?

Sharpen Geometry Skills with Quick Test

Difficulty: Moderate
Grade: Grade 4
Study OutcomesCheat Sheet
Colorful paper art promoting a Polygon or Not practice quiz for middle school students.

Which of the following figures is not a polygon?
Pentagon
Triangle
Circle
Rectangle
A polygon is defined as a closed figure with straight sides. A circle does not have straight sides, so it is not considered a polygon.
What defines a polygon?
An open shape with curves
A figure with only one curved boundary
A shape with only curved edges
A closed figure with three or more straight sides
A polygon is characterized by having a closed boundary and being composed entirely of straight line segments. This definition excludes any shape with curves or an open form.
Which of the following is considered a polygon?
Circle
Oval
Ellipse
Square
A square is a polygon because it is a closed figure made up of straight sides. The other options involve curves, disqualifying them as polygons.
How many sides does a triangle have?
Two
One
Three
Four
By definition, a triangle is a polygon with three sides. This is one of the most basic properties distinguishing it from other shapes.
What is the name of the quadrilateral with four equal sides and four right angles?
Rhombus
Trapezoid
Square
Rectangle
A square is defined as a quadrilateral with all sides equal and all angles at 90 degrees. Although a rhombus has equal sides, it does not necessarily have right angles, making the square the correct answer.
Which characteristic is not required for a shape to be classified as a polygon?
Having at least three sides
Having curved edges
Being a closed figure
Having only straight sides
Polygons must be closed figures with straight sides and have at least three sides. The presence of curved edges is not a requirement and, in fact, disqualifies a shape from being a polygon.
What is the formula for calculating the sum of interior angles of an n-sided polygon?
n * 180
(n - 2) * 90
(n + 2) * 180
(n - 2) * 180
The sum of the interior angles of an n-sided polygon is determined by dividing the polygon into triangles. The correct formula, (n - 2) * 180, reflects the fact that a polygon can be split into (n - 2) triangles.
A concave polygon differs from a convex polygon in that it has:
All sides equal
All interior angles less than 180°
A curved side
At least one reflex angle greater than 180°
A concave polygon contains at least one interior angle that is greater than 180°, known as a reflex angle. This feature is what sets it apart from convex polygons, where all interior angles are less than 180°.
How many diagonals does a pentagon have?
5
7
10
8
The formula for the number of diagonals in a polygon is n(n - 3)/2. For a pentagon, where n equals 5, the computation yields 5 diagonals.
Which property must hold true for a shape to be considered a regular polygon?
Only the sides are equal
All sides and interior angles are equal
All sides and angles are different
All interior angles are equal but sides can vary
A regular polygon is defined by having both equal side lengths and equal interior angles. This consistency in measures is essential for classifying a polygon as regular.
If a hexagon is regular, what is the measure of each interior angle?
120°
140°
100°
90°
The measure of each interior angle in a regular n-sided polygon can be calculated using the formula ((n - 2) * 180)/n. For a hexagon, substituting n = 6 gives an interior angle of 120°.
Which of the following shapes can never be considered a polygon?
Triangle
Rectangle
Hexagon
Circle
A circle is not classified as a polygon because it lacks straight sides and a series of vertices. All the other shapes listed are made up of straight lines and satisfy the definition of a polygon.
What is the minimum number of sides required for a shape to be classified as a polygon?
3
4
1
2
By definition, a polygon must have at least three sides. This requirement distinguishes polygons from simpler geometric figures such as line segments.
Which of the following is true about the sum of exterior angles of any polygon?
It depends on the number of sides
It equals 180°
It equals 720° for quadrilaterals
It equals 360°
The sum of the exterior angles of any polygon is universally 360°, regardless of the number of sides. This is a fundamental property that applies to all polygons.
Which of the following statements is true about simple polygons?
They can intersect themselves
They must have all sides equal
They do not cross over themselves
They have only curved edges
Simple polygons are defined by the fact that their sides do not intersect except at the vertices. This non-intersecting property ensures a well-defined interior and exterior.
Why is a star-shaped figure not classified as a simple polygon?
Because it is not a closed figure
Because it has more than five sides
Because it contains curved sections
Because its sides intersect at points other than the vertices
A simple polygon is one in which the sides only meet at their endpoints and do not cross over each other. In a star-shaped figure, additional side intersections occur, which disqualifies it from being classified as a simple polygon.
For a decagon, how many distinct diagonals are present?
30
35
45
40
The number of diagonals in an n-sided polygon is determined by the formula n(n - 3)/2. For a decagon where n is 10, this formula results in 35 diagonals.
In a regular polygon, if each exterior angle measures 30°, how many sides does it have?
12
10
15
18
Since the sum of the exterior angles of any polygon is always 360°, dividing 360° by the measure of each exterior angle (30°) yields the number of sides. In this case, the polygon has 12 sides.
Which of the following polygons is always cyclic?
Irregular quadrilateral
Regular pentagon
Self-intersecting star polygon
Concave polygon
A cyclic polygon is one whose vertices all lie on a single circle. Regular polygons, such as a regular pentagon, have the symmetry necessary for all vertices to be concyclic, unlike irregular or self-intersecting polygons.
What concept allows the decomposition of an n-sided polygon into triangles, and how many triangles are formed?
Segmentation; n-1 triangles
Partitioning; n-3 triangles
Triangulation; n-2 triangles
Diagonal counting; n triangles
Triangulation is the method used to break down a polygon into triangles by drawing non-intersecting diagonals from one vertex. An n-sided polygon will always be divided into n-2 triangles through this process.
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Study Outcomes

  1. Analyze geometric figures to distinguish between polygons and non-polygons.
  2. Identify the key characteristics that define a polygon.
  3. Apply knowledge of shape properties to classify unfamiliar figures.
  4. Evaluate and compare geometric figures based on side count and angle structures.

Polygon Quiz: Which Figure Isn't a Polygon Cheat Sheet

  1. Understanding Polygons - A polygon is a closed, two-dimensional shape formed by straight line segments, ranging from simple triangles to complex decagons. These shapes are everywhere, from stop signs to soccer balls, and kick off your geometry journey! Learn more on Britannica
  2. Classifying by Sides - Polygons get their names from how many sides they have: triangles (3), quadrilaterals (4), pentagons (5), and so on. Spotting these in architecture and art sharpens your recognition skills! Dive into classifications on Math is Fun
  3. Regular vs Irregular - Regular polygons boast equal sides and equal angles, like perfect equilateral triangles or squares. Irregular ones mix things up with varying lengths and angles, keeping you on your toes! Explore regular polygons on SplashLearn
  4. Interior Angle Sum - The sum of interior angles in an n‑sided polygon follows (n - 2) × 180°. For instance, a hexagon's interior angles add up to 720°, revealing hidden patterns in each shape. See the formula on GeeksforGeeks
  5. Exterior Angle Formula - Every regular polygon shares a simple trick: each exterior angle is 360° ÷ n. A regular pentagon's angles each measure 72°, rounding out its glossy form. Check out the details on GeeksforGeeks
  6. Convex vs Concave - Convex polygons boast all interior angles under 180°, bulging outward like a friendly smile. Concave ones tuck in a "cave," featuring at least one reflex angle over 180°. Discover more on Math is Fun
  7. Perimeter Power - To find a regular polygon's perimeter, just multiply the number of sides (n) by the side length (s): Perimeter = n × s. A hexagon with 4 cm sides stretches 24 cm around! Perimeter formulas on GeeksforGeeks
  8. Area Adventures - The area of a regular polygon is (n × s × apothem) ÷ 2, where the apothem is the distance from center to side midpoint. This unlocks the inner space of your shape! Explore area formulas on GeeksforGeeks
  9. Why Not a Circle? - Circles aren't polygons because they lack straight edges; polygons are built from straight line segments that meet at angles. It's all about those crisp corners! Read the definition on Math is Fun
  10. Name Origins - "Polygon" hails from Greek: "poly" means "many" and "gon" means "angle," perfectly capturing shapes with multiple corners. Next time you draw a star, thank the ancients! See the etymology on Merriam-Webster
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