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Polygons

The problems in this category require knowledge of the properties
of regular and nonregular polygons. Measures of interior,
exterior, and central angles form the basis of many of the problems.
Many of the problems in this category will require advanced knowledge
and an integration of several geometric topics.
Problems about
triangles and
quadrilaterals
are listed in their own categories.
 Related Resources

Interactive resources from our Math Tools project:
Geometry: Polygons
The closest match in our Ask Dr. Math archives:
High School: Triangles/Polygons
NCTM Standards:
Geometry Standard for Grades 912
Access to these problems requires a Membership.

Beyond Exterior Angles
 Annie Fetter

Geometry, difficulty level 2. Extend two sides of the given polygon and determine the angle at which
the new lines meet.
... more>>

Building a Regular Hexagon
 Annie Fetter and Steve Weimar

Geometry, difficulty level 3. How do you form a regular hexagon by attaching rectangles to the sides
of an equilateral triangle?
... more>>

Build Your Own Hexagon
 Annie Fetter

Geometry, difficulty level 2. Put a square on each edge of an equilateral triangle (edgelength one unit) and connect the outside vertices of adjacent squares to form a hexagon. Is this hexagon equilateral? equiangular? What is its area?
... more>>

Constructing a Window
 Annie Fetter

Geometry, difficulty level 4. Explain the shapes of the other four sides of a regular hexagonal window that's built between two wall studs 22.5" apart.
... more>>

Drawing a Kite Plan
 Annie Fetter

Geometry, difficulty level 3. Given a picture of a kite plan, figure out the radius of the circle that creates the curved section.
... more>>

Drawing Out a Decagon
 Annie Fetter

Geometry, difficulty level 2. Extend sides AB and IH of the regular decagon ABCDEFGHIJ until they intersect. What is the measure of the acute angle at this intersection?
... more>>

Examining an Octagon
 Annie Fetter

Geometry, difficulty level 3. Describe the rectangles that you would need to put on the sides of a square in order to be able to end up with a regular octagon when you connect the outside vertices of the figure.
... more>>

Extending the Enneagon
 Annie Fetter

Geometry, difficulty level 3. Extend the sides AB and ED of the regular enneagon ABCDEFGHI until they intersect. What is the measure of the acute angle at this
intersection? Extend sides AB and EF. Now what's the measure of that acute angle at the intersection?
... more>>

Fix This Picture
 Annie Fetter

Geometry, difficulty level 2. Figure out what's wrong with this picture that includes a circle and a rhombus.
... more>>

Going Global
 Annie Fetter & NCTM's WLME

Geometry, difficulty level 2. Look at Shakespeare's Globe Theater from a mathematical standpoint  figure out the interior angle of an icosagon and calculate how many people could stand in the "field" in front of and around the stage.
... more>>

Pentagon Puzzle
 Annie Fetter

Geometry, difficulty level 1. Explore the interior angles of pentagons.
... more>>

Playing with a Pentadecagon
 Annie Fetter

Geometry, difficulty level 2. Extend the sides AB and ED of the regular pentadecagon ABCDEFGHIJKLMNO
until they intersect. What is the measure of the angle at this
intersection?
... more>>

Regional Ratios
 Annie Fetter

Geometry, difficulty level 2. A regular hexagon and an equilateral triangle have the same perimeter. What's the ratio of their areas?
... more>>

Seeing Stars
 Annie Fetter

Geometry, difficulty level 2. Find the measure of the angle at the "star points" of a "regular star"
when the star has five sides. How about when the star has eight sides?
... more>>

Studying Stars
 Annie Fetter

Geometry, difficulty level 2. Given a number of points spaced around a circle, how many lines does it take to connect each point to all the other points except for the ones next to it?
... more>>

What's This Polygon?
 Annie Fetter

Geometry, difficulty level 4. Triangle PQR is inscribed in a circle. If PR is a side of a 21sided inscribed regular polygon, PQ is a side of a 28sided incribed regular polygon, and QR is a side of an nsided inscribed regular polyon, find a possible value for n.
... more>>
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