How to Draw an Easy Square How to Construct a Hexagon

Regular hexagon, given one side

How to construct a regular hexagon given one side. The construction starts by finding the center of the hexagon, then drawing its circumcircle, which is the circle that passes through each vertex. The compass then steps around the circle marking off each side.

Printable step-by-step instructions

The above animation is available as a printable step-by-step instruction sheet, which can be used for making handouts or when a computer is not available.

Explanation of method

This construction is very similar to Constructing a hexagon inscribed in a circle, except we are not given the circle, but one of the sides instead. Steps 1-3 are there to draw this circle, and from then on the constructions are the same.

The center of the circle is found using the fact that the radius of a regular hexagon (distance from the center to a vertex) is equal to the length of each side. See Definition of a Hexagon.

Proof

The image below is the final drawing from the above animation.

	Argument	Reason
1	ABCDEF is a hexagon	It is a polygon with six sides. See Definition of a Hexagon.
2	AB, BC, CD, DE, EF, FA are all congruent.	Drawn with the same compass width AF.
3	A, B, C, D, E, F all lie on the circle O	By construction
4	ABCDEF is a regular hexagon	From (1), (2). All its vertices lie on a circle, and all sides are congruent. This defines a regular hexagon. See Regular polygon definition and properties

- Q.E.D

Try it yourself

Click here for a printable worksheet containing two problems to try. When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.

Other constructions pages on this site

List of printable constructions worksheets

Lines

Introduction to constructions
Copy a line segment
Sum of n line segments
Difference of two line segments
Perpendicular bisector of a line segment
Perpendicular at a point on a line
Perpendicular from a line through a point
Perpendicular from endpoint of a ray
Divide a segment into n equal parts
Parallel line through a point (angle copy)
Parallel line through a point (rhombus)
Parallel line through a point (translation)

Angles

Bisecting an angle
Copy an angle
Construct a 30° angle
Construct a 45° angle
Construct a 60° angle
Construct a 90° angle (right angle)
Sum of n angles
Difference of two angles
Supplementary angle
Complementary angle
Constructing 75° 105° 120° 135° 150° angles and more

Triangles

Copy a triangle
Isosceles triangle, given base and side
Isosceles triangle, given base and altitude
Isosceles triangle, given leg and apex angle
Equilateral triangle
30-60-90 triangle, given the hypotenuse
Triangle, given 3 sides (sss)
Triangle, given one side and adjacent angles (asa)
Triangle, given two angles and non-included side (aas)
Triangle, given two sides and included angle (sas)
Triangle medians
Triangle midsegment
Triangle altitude
Triangle altitude (outside case)

Right triangles

Right Triangle, given one leg and hypotenuse (HL)
Right Triangle, given both legs (LL)
Right Triangle, given hypotenuse and one angle (HA)
Right Triangle, given one leg and one angle (LA)

Triangle Centers

Triangle incenter
Triangle circumcenter
Triangle orthocenter
Triangle centroid

Circles, Arcs and Ellipses

Finding the center of a circle
Circle given 3 points
Tangent at a point on the circle
Tangents through an external point
Tangents to two circles (external)
Tangents to two circles (internal)
Incircle of a triangle
Focus points of a given ellipse
Circumcircle of a triangle

Polygons

Square given one side
Square inscribed in a circle
Hexagon given one side
Hexagon inscribed in a given circle
Pentagon inscribed in a given circle

Non-Euclidean constructions

Construct an ellipse with string and pins
Find the center of a circle with any right-angled object

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Source: https://www.mathopenref.com/consthexagon.html