Math Worksheet: Polygons and Circles (With PDF)

What is a Polygon?

A polygon is a two-dimensional closed figure made up of only straight line segments. It is a geometric figure with three or more sides. Triangles (3 sides), Quadrilaterals (4 Sides), Pentagons (5 Sides), Hexagons (6 sides), Heptagons (7 Sides), Octagons (8 sides), Decagons (10 sides), etc. are all examples of polygons. A polygon having all its sides equal is called regular polygons. If all sides are not equal, it is called irregular polygons. Refer to Fig. 1.

Example of Polygons
Fig. 1: Example of Polygons

What is a Circle?

A circle is a closed figure made with curved lines such that all points of the curve are at a fixed distance from a point. This fixed point is called the center of the circle. Refer to Fig. 2. Remember the following points with respect to a circle.

  • The radius of a circle is a line segment that joins the center of the circle to any point on the circle. There are many radii of equal length in any circle.
  • The diameter of any circle is twice the length of the radius.
  • A line joining any two points on the circle is called a chord. The largest chord passes through the center of the circle and called the diameter of the circle.
Examples of Circles
Fig. 2: Examples of Circles

Polygons and Circle Worksheet

1. Answer the following questions related to polygons and circles?

a. What is a circle?
b. What is the name given to the largest chord?
c. What is the difference between a quadrilateral, a rectangle, and a square?
d. What is a polygon?
e. Which instrument do you use to draw a circle?
f. How many sides does an octagon have?
g. How many diameters do a circle have?
h. What is the difference between a chord and a radius of a circle?
i. Draw two points A and B in your sheet. Now Add A and B to make a line segment. Now let’s assume that while measuring this line segment with a scale, you kept point at 3 cm mark and you find point B at 9 cm mark. So what is the length of line segment AB?
j. How many straight sides does a circle have?

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2. Fill in the blanks with correct answer from your understanding about polygons and circles?

a. A polygon having all sides of equal length is called a ________ Polygon.
b. The radius of a circle is _________ the diameter.
c. The length around a circle is called its_____________ .
d. A____________ sided polygon is called a Pentagon.
e. A___________________ is a special quadrilateral in which opposite sides are equal.
f. If the diameter of a wheel is 120 cm, its radius is________ cm.

g. The surface of a circle is called __________ surface.
h. The diameter of a circle with a radius of 60 mm is___________ cm.

i. A closed figure made up of only straight line segments is called a_________.
j. A line that connects the centre of the circle to a point on the circle is called

3. Read the following statements related to polygons and circles and Write T for true and F for False

a. A rectangle is a quadrilateral.
b. A circle is a type of polygon.
c. A hexagon is a closed figure.
d. A diameter divides a circle into two equal parts.
e. A circle is an open figure.
f. Circumference of a circle is always longer than its diameter.
g. A triangle is a Polygon.
h. A Scale is used to draw a circle.
i. All rectangles are quadrilaterals but all quadrilaterals are not rectangles.
j. A heptagon has six sides.

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4. Mixed questions about polygons and circles?

a. How many sides does a polygon have?
b. What is the name of the polygon with seven vertices?
c. What is the sum of the number of vertices and the number of sides of an Octagon?
d. A hexagon has six angles. True or false?
e. All the angles of a regular triangle are equal. True or False?
f. A regular pentagon has more number of sides than an irregular pentagon. True or False.
g. What is the length of the biggest chord of a circle with a radius of 15 cm?
h. A circle has many radii of different lengths. True or False?
i. If the circumference of two different circles is equal, their radius will be equal. True or false?
j. What is the meaning of a circumference of a circle?

5. Refer to the below image (Fig. 3) and write the names of the geometric shapes for polygons and circles.

Polygons and Images
Fig. 3: Polygons and Images

6. Refer to Fig. 4 and answer the questions below it

Explanation of Circle
Fig. 4: Explanation of Circle

a. Name of line segment AB is ___________
b. Length of segment AO=Length of segment OD. True or False?
c. AC is the longest line segment that can be drawn in the given figure. True or False?
d. Curved length ABC is equal to Curved length ADC. True or False?
e. If the length of AOC is 24 cm. what is the length of OD in mm?

Few more useful worksheets for you:

Subtraction Worksheet
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Polygon and Circle Worksheet
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