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Quizzes > Mathematics > Geometry

Polygon Sides Quiz: Can You Classify Them All?

Curious how many sides has a heptagon have or how many sides do nonagon have? Test yourself now!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration for polygon knowledge quiz on a golden yellow background

Use this quick quiz to learn how many sides a heptagon has and how it stacks up against shapes like a nonagon. You'll answer short questions to lock in side counts, then check polygon side counts or take the full polygon quiz for more practice.

How many sides does a heptagon have?
9
6
7
8
A heptagon is defined as a seven-sided polygon. The prefix hepta- originates from Greek, meaning seven. In geometry, any seven-sided closed figure is called a heptagon. For more details, see .
What is the name of a polygon with eight sides?
Heptagon
Hexagon
Nonagon
Octagon
An eight-sided polygon is known as an octagon. The term derives from the Greek words okto, meaning eight, and gonia, meaning angle. Stop signs in many countries are regular octagons. Learn more at .
Which polygon has nine sides?
Heptadecagon
Octagon
Nonagon
Decagon
A nine-sided polygon is called a nonagon, also known as an enneagon. The prefix nona- or ennea- signifies nine in Latin and Greek, respectively. Nonagons are less common but appear in certain architectural designs. See for more information.
What is the sum of the interior angles of a heptagon?
720
540
1080
900
The sum of interior angles in an n-sided polygon is (n ? 2) 180. For a heptagon, n = 7, so the calculation is (7 ? 2) 180 = 900. This holds true for any simple heptagon. More details at .
How many diagonals does a heptagon have?
21
7
28
14
The number of diagonals in an n-sided polygon is given by n(n ? 3)/2. For n = 7, thats 7 4 / 2 = 14 diagonals. A diagonal connects two nonadjacent vertices. See for more.
In a regular heptagon, what is the measure of one exterior angle?
51.43
45
60
70
Each exterior angle of a regular polygon equals 360/n. For a heptagon, n = 7, so 360 7 ? 51.43. All exterior angles in a regular heptagon are congruent. More info at .
For a regular nonagon, what is the measure of one interior angle?
160
180
120
140
A regular nonagon has interior angles summing to (9 ? 2)180 = 1260, and each of the 9 angles measures 1260/9 = 140. This formula applies to any regular polygon. Read more at .
Which polygon has exactly 20 diagonals?
Heptagon
Octagon
Decagon
Nonagon
The diagonal formula n(n ? 3)/2 yields 20 when n = 8: 85/2 = 20. Thus an octagon has 20 diagonals. Heptagons and nonagons have 14 and 27 diagonals, respectively. See .
How many triangles can be formed by choosing any three vertices of a heptagon?
42
35
21
28
The number of triangles from n vertices is given by the binomial coefficient C(n,3). For n = 7, C(7,3) = 35. Each selection of three distinct vertices defines a triangle. More details: .
A regular heptagon is inscribed in a circle of radius r. Which formula gives its side length s in terms of r?
s = 2r cos(?/7)
s = 2r tan(?/7)
s = 2r sin(?/7)
s = r
For a regular n-gon inscribed in a circle of radius r, each side s = 2rsin(?/n). When n = 7, this gives s = 2r sin(?/7). This derives from the law of sines in the isosceles triangle formed by two radii and one side. See .
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Study Outcomes

  1. Identify the number of sides in a heptagon -

    Answer both common queries "how many sides to a heptagon" and "how many sides has a heptagon have" by confirming that this seven-sided polygon features seven edges and vertices.

  2. Recall the sides of a nonagon -

    Memorize and confidently state the answer to "how many sides do nonagon have", recognizing that a nonagon has exactly nine sides in total.

  3. Apply polygon naming rules -

    Use prefixes and numerical patterns to deduce the number of sides for polygons beyond heptagons and nonagons, such as decagons or dodecagons.

  4. Analyze side-count progressions -

    Compare and contrast polygons by tracking how side counts increase with each additional prefix, strengthening your shape classification skills.

  5. Engage with interactive quizzes -

    Test your polygon IQ in real time with fun, free quiz questions that reinforce your understanding of shape properties.

  6. Evaluate learning progress -

    Review immediate feedback on quiz responses to identify areas for improvement and boost your confidence in geometry basics.

Cheat Sheet

  1. Understanding Polygon Nomenclature -

    The term "heptagon" comes from the Greek prefix hepta - meaning seven and gonia meaning angle, so knowing how many sides to a heptagon is as simple as matching its prefix to the number 7. In the same way, understanding how many sides do nonagon have comes from its nona - prefix that denotes nine. This naming pattern applies consistently across polygons, from tetragon (4) up to dodecagon (12) and beyond.

  2. Sum of Interior Angles Formula -

    Use the formula (n − 2) × 180° to find the total interior angle sum of any n-sided polygon - so a heptagon's sum is (7 − 2) × 180° = 900° and a nonagon's is (9 − 2) × 180° = 1260°. This key relation appears in virtually every high school and university geometry textbook, including Euclid's Elements and modern resources like Stewart's Calculus. Mastering it helps you verify your side counts through angle measures.

  3. Individual Interior Angle of Regular Polygons -

    In a regular n-gon, each interior angle equals [(n − 2) × 180°] / n, giving about 128.57° for a regular heptagon and exactly 140° for a regular nonagon. This formula, featured in college geometry courses, lets you see at a glance why some shapes tessellate (like hexagons) and others do not. Working through a few examples cements the link between side count and angle size.

  4. Counting Diagonals Efficiently -

    The number of diagonals in an n-sided polygon follows n(n − 3)/2, yielding 14 diagonals for a heptagon and 27 for a nonagon. Drawing these diagonals can solidify how the sides connect, reinforcing the concept of how many sides has a heptagon have in relation to vertex connections. This combinatorial approach is also covered in discrete math and combinatorics syllabi.

  5. Mnemonic Tricks and Real-World Examples -

    Memory aids like "Heppy Seven" for heptagon and "Nona the Cat with Nine Lives" for nonagon make recall both playful and efficient. Spot real-world heptagons in seven-segmented road signs or architectural features like the UK's seven-sided bollards, and nonagons in international stop-sign variants. Linking shapes to everyday objects shows that polygons aren't just abstract - they're all around us.

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