Math Forum - Problems Library - Geometry - Polygons

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Geometry
  lines/angles
  triangles
  quadrilaterals
  polygons
  circles
  perimeter, area,
    volume
  similar/congruent
  right triangles
  transform/symmetry
  construction/locus
  coordinate geometry
  modeling/applications

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Geometry
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Geometry
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Polygons
The problems in this category require knowledge of the properties of regular and non-regular 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 9-12


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 21-sided inscribed regular polygon, PQ is a side of a 28-sided incribed regular polygon, and QR is a side of an n-sided inscribed regular polyon, find a possible value for n. ... more>>

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