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Polygons Quiz - CBSE Class 7 Mathematics

Free practice quiz: Polygons (CBSE Class 7 Mathematics). 18 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 7 Mathematics practice quiz has 18 multiple-choice questions on Polygons, and 18 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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What makes a polygon

  • A polygon is a simple closed figure made only of straight line segments that meet at their ends.
  • Open figures, figures with curved parts, and figures whose sides cross are not polygons.
  • A convex polygon has every interior angle less than a straight angle. A concave polygon has at least one reflex interior angle.

Common mistake: Calling a figure with a curved side, or an open figure, a polygon just because it has some straight sides.

Naming polygons and regular polygons

  • Polygons are named by their number of sides, for example quadrilateral (4 sides) and heptagon (7 sides).
  • A regular polygon has all sides equal AND all interior angles equal.
  • A polygon with n sides also has n vertices and n interior angles.
Sides, vertices and angles are equal in number
\[\text{sides} = \text{vertices} = \text{angles} = n\]

Common mistake: Thinking equal sides alone make a polygon regular. A rhombus has equal sides but is not regular unless its angles are also equal.

Sum of interior angles

  • Diagonals drawn from one vertex split an n-sided polygon into (n − 2) triangles.
  • Each triangle adds two right angles, so the angle sum increases as the number of sides increases.
Number of triangles formed from one vertex
\[n - 2\]
Sum of interior angles (n sides)
\[(2n - 4) \times 90^\circ\]

Common mistake: Multiplying by n instead of (n − 2), for example taking a quadrilateral's angle sum as 4 straight angles.

Angles of a regular polygon

  • In any polygon, the exterior angles (one at each vertex) always add up to 360°.
  • In a regular polygon all exterior angles are equal. Each interior and exterior angle pair forms a straight angle.
Sum of exterior angles
\[360^\circ\]
Each exterior angle (regular)
\[\frac{360^\circ}{n}\]
Each interior angle (regular)
\[\frac{(2n - 4) \times 90^\circ}{n}\]
Interior and exterior angle at a vertex
\[\text{interior} + \text{exterior} = 2 \times 90^\circ\]

Common mistake: Dividing 360° by n to get the interior angle. That gives the exterior angle, not the interior angle.

Counting diagonals

  • A diagonal joins two vertices that are not next to each other.
  • From one vertex you cannot draw a diagonal to that vertex itself or to its two neighbours.
Diagonals from one vertex
\[n - 3\]
Total diagonals
\[\frac{n(n - 3)}{2}\]

Common mistake: Forgetting to divide by 2 for the total. Each diagonal gets counted twice, once from each of its ends.

Exam tips

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

  1. What is a polygon?

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    Answer: B. A closed figure with straight sides

    A polygon is defined as a closed figure that is formed by joining straight line segments.

  2. What is the name of a polygon with six sides?

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    Answer: A. Hexagon

    A polygon with six sides is called a hexagon.

  3. What is the exterior angle of a regular octagon?

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    Answer: A. 45 degrees

    The formula for calculating the exterior angle of a regular polygon is 360/n, where n is the number of sides. For an octagon, it's 360/8 = 45 degrees.

  4. How many sides does a nonagon have?

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    Answer: C. 9

    A nonagon is a polygon that has nine sides.

  5. What is the interior angle of a regular decagon?

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    Answer: A. 144 degrees

    The measure of interior angles of a regular polygon can be found using the formula [(n - 2) × 180]/n. For a decagon (10 sides), it's 144 degrees.

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More questions in this quiz

Answers and explanations are in the full quiz.

  1. How many sides does a pentagon have?
  2. What is the sum of the interior angles of a triangle?
  3. How many diagonals can be drawn from one vertex of a hexagon?
  4. What is a regular polygon?
  5. How many sides does a dodecagon have?
  6. What is the area of a regular hexagon with side length 's'?
  7. What type of triangle has all sides of different lengths?
  8. Which of the following is not a polygon?
  9. What is the relationship between the sum of the interior angles and the number of sides in a polygon?
  10. Which polygon has the largest area for a given perimeter?
  11. Which of the following polygons is concave?
  12. In a regular polygon, what is the formula to find the measure of each interior angle?
  13. What is the most complex regular polygon?

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