Mathematics
Grade 5
15 min
Construct a regular hexagon inscribed in a circle (Tutorial Only)
Construct a regular hexagon inscribed in a circle (Tutorial Only)
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the parts of a circle (center, radius, circumference).
Define a regular hexagon and an inscribed polygon.
Use a compass to draw a circle and mark arcs accurately.
Use a straightedge to connect points to form straight sides.
Construct a regular hexagon inscribed in a given circle.
Explain why the side length of an inscribed regular hexagon equals the circle's radius.
Appreciate the precision required in geometric constructions.
Have you ever seen a honeycomb 🐝 or a stop sign? They have a special shape with six equal sides! Today, we'll learn how to draw this amazing shape perfectly inside a circle.
In this lesson, you'll discover how to use a compass and a straightedge to construct a regular hexagon that fits perfectly inside a...
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Key Concepts & Vocabulary
TermDefinitionExample
CircleA round shape where all points on the edge are the same distance from a central point.A hula hoop or the edge of a pizza.
RadiusThe distance from the center of a circle to any point on its edge.If you draw a line from the middle of a pizza to its crust, that's a radius.
HexagonA polygon (a closed shape with straight sides) that has exactly six sides and six angles.A stop sign is a common example of a hexagon.
Regular HexagonA hexagon where all six sides are the same length, and all six angles are the same size.The shape of a perfectly cut hexagonal floor tile.
InscribedWhen a shape is drawn inside another shape so that its vertices (corners) touch the boundary of the outer shape.A square drawn inside a circle so its corners touch the circle's edge.
Co...
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Core Formulas
Radius Property of a Circle
$r_1 = r_2 = r_3 = \dots$
All radii of the same circle are equal in length. This means that no matter where you draw a line from the center to the edge of a circle, its length will always be the same. This is crucial for setting your compass correctly.
Hexagon Side Length Property
$s = r$
The side length ($s$) of a regular hexagon inscribed in a circle is equal to the radius ($r$) of that circle. This is the secret to constructing the hexagon! If you set your compass to the radius of the circle, you can use that exact opening to mark off the six vertices of the hexagon around the circle's edge.
4 more steps in this tutorial
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Challenging
If you construct a regular hexagon inside a circle and then draw a line from the center of the circle to each of the hexagon's 6 vertices, what kind of smaller shapes are formed inside the hexagon?
A.6 equilateral triangles
B.6 right triangles
C.3 rectangles
D.2 trapezoids
Challenging
You are given a circle with center O and radius r. You place your compass point on the circumference at point P and make an arc that intersects the circle at point Q. What is the relationship between the lengths of the lines OP, OQ, and PQ?
A.OP is longer than OQ and PQ
B.All three lengths are equal to the radius, r
C.PQ is twice as long as OP
D.OQ is shorter than OP and PQ
Challenging
A friend claims they can construct a perfect inscribed regular hexagon using only a straightedge, but no compass. Why is this impossible according to the tutorial's method?
A.straightedge can't draw the initial circle.
B.straightedge can't measure the radius and accurately transfer that distance to mark the vertices.
C.straightedge can't draw curved lines.
D.Both A and B are correct.
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