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PreAlgebra
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Geometry in the Plane

Problems in this category require students to describe, classify, and understand the relations that exist among twodimensional objects. They may require students to think in terms of the
coordinate plane or understanding of congruence, similarity, the Pythagorean theorem, symmetry, or tessellations.
Some of these problems are also in the following subcategories:
 Related Resources

Interactive resources from our Math Tools project:
Math 7: Geometry in the Plane
The closest match in our Ask Dr. Math archives:
Middle School: Two Dimensional Geometry
NCTM Standards:
Geometry Standard for Grades 68
Access to these problems requires a Membership.

3D Vision
 Annie Fetter

PreAlgebra, difficulty level 3. When you fold up the given net of a cube, what shape is formed by the segments on the faces of the cube?
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All the Similar Triangles
 Annie Fetter

PreAlgebra, difficulty level 3. How would you place points D and E to make similar triangles?
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Back Yard Trees
 Judy Ann Brown

PreAlgebra, difficulty level 4. How many different quadrilaterals can be formed by joining any four of the nine trees?
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Bella's Bagel Bakery
 Suzanne Alejandre

PreAlgebra, difficulty level 1. How much more area is covered with cream cheese on the large bagel
than on the small bagel?
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Building Fences
 Judy Ann Brown

PreAlgebra, difficulty level 3. Plan a garden so as to maximize the area surrounded by a 36yard fence.
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Building on Water
 Judy Ann Brown

PreAlgebra, difficulty level 4. Find the area of a circular pond not covered by a rectangular building.
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Canadian Soccer
 Judy Ann Brown

PreAlgebra, difficulty level 2. Find the distance a player runs to complete three "Double V" laps.
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Chamique the Archer
 Mr. Marthinsen's Geometry Class

PreAlgebra, difficulty level 3. Chamique wants to know the probability of hitting a bull'seye with a randomly shot arrow.
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Coloring a Hexagon
 Ranjan Rohatgi, Spencer Koerner, Suzanne Alejandre

PreAlgebra, difficulty level 2. How many different ways of coloring the hexagon are represented in
Spencer's drawing?
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Exploring Area
 Judy Ann Brown

PreAlgebra, difficulty level 4. Find information about Pick's theorem and solve an area problem using this method.
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Fences for Fido and Friends
 Annie Fetter

PreAlgebra, difficulty level 2. Find the area of each rectangular dog pen.
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Forming Triangles from a Folding Ruler
 Annie Fetter, Suzanne Alejandre

PreAlgebra, difficulty level 1. Describe the three triangles that can be made with the full length of
a 6 foot long folding wooden ruler.
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Graphing for Area
 Judy Ann Brown

PreAlgebra, difficulty level 2. Graph six points and find the area of the resulting hexagon.
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Graphs
 Suzanne Alejandre, Annie Fetter

PreAlgebra, difficulty level 3. Match the descriptions to the graphs. Explain how to find one of the points on each graph and give the labels for the x and yaxes.
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How Fast Is a Minute?
 Suzanne Alejandre

PreAlgebra, difficulty level 1. How many feet does the tip of the minute hand travel in an hour on the
clock on Philadelphia's City Hall Tower?
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How Wide Is My Garden?
 Judy Ann Brown

PreAlgebra, difficulty level 3. A scale drawing is used to determine the width and area of a garden.
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I'm a Groundhog?
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Using Suzanne's height, Phil's height, and Suzanne's shadow length, find Phil's shadow length.
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Lillian's Lines
 Lillian Ray and Molly Ribble

PreAlgebra, difficulty level 3. Students are asked to find how many square panes a path goes through
for a window of a
given size.
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Lincoln's Top Hat
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Find the dimensions of a rectangular sheet of paper used to make a paper top hat that has width and height the same.
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Measuring a Mountain Bike
 Annie Fetter

PreAlgebra, difficulty level 3. Help Annie determine the circumference of her bike tire so that she
can accurately set up her
new cyclometer.
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Mirror Musing
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Using the information given in a picture of Hagrid and Baby Norbert, find out how tall each of them is.
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Office Tile Choice
 Judy Ann Brown

PreAlgebra, difficulty level 3. Find the total cost of purchasing tiles for my office.
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Partial Area
 Judy Ann Brown

PreAlgebra, difficulty level 3. Find the area of the portion of the circle that is not included inside the inscribed square.
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Paving Stones
 Suzanne Alejandre

PreAlgebra, difficulty level 1. How many stones did Kathy need to buy to pave an area in her yard?
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Peanut's Back Yard
 Jonathan Bauer

PreAlgebra, difficulty level 3. Peanut, the overexcited dog, makes 40 laps around a stake and travels a total distance of 1 mile. If his bowl of water is 20 feet away from the stake, can he get a drink?
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PicturePerfect Geometry
 Judy Ann Brown

PreAlgebra, difficulty level 2. Graph four points and name the figure that you have drawn.
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Pizza Pie
 Judy Ann Brown

PreAlgebra, difficulty level 3. Use the given information to decide how many slices of the small pizza would be equal to or greater than 3 slices from the large pizza.
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Practicing for the Winter Olympics
 Cynthia Paul

PreAlgebra, difficulty level 2. What is the length of the semicircular path Sonya skates across the
ice rink?
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Quilting Squares
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Help with some quick calculations of the amount of fabric needed for this quilt design.
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A Quilt Made of Squares
 Annie Fetter

PreAlgebra, difficulty level 3. Using the information given, will the finished quilt be in the shape of a
square?
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Right Triangle, Which Legs?
 Annie Fetter

PreAlgebra, difficulty level 3. Find the possible lengths for the third side of a right triangle given
the lengths of the other two sides.
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Riz's Route
 Richard Tchen & Steve Risberg

PreAlgebra, difficulty level 3. Where is Riz standing when he realizes it would be the same distance to
continue walking
on the longer path as it would be to turn around and take the shortcut?
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Shapes Rock
 Judy Ann Brown

PreAlgebra, difficulty level 3. Find the number of diagonals in a polygon of 40 sides.
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Shine On Harvest Moon
 Judy Ann Brown

PreAlgebra, difficulty level 2. Find the area of the largest circle that can be cut from a nineinch by twelveinch sheet of paper.
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Shortcut Savings
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Find a rule to tell how much distance I will save when I take the shortcut.
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A Stellar Garden
 Bill Marthinsen

PreAlgebra, difficulty level 3. Martha Stewart wants to rebuild her ugly garden. She needs help calculating the areas in the new garden.
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Symmetry Surprise
 Annie Fetter, Suzanne Alejandre

PreAlgebra, difficulty level 3. Identify the types of symmetries of each of three patterns.
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Tiling Triangles
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Given the dimensions of a large triangle, find the dimensions of the 25 small triangles that tile it.
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Timber!
 Steve Risberg

PreAlgebra, difficulty level 3. A tree breaks threeeighths of the way up the trunk, and the tip hits the ground 40 feet from the base of the trunk. How tall was the tree?
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Twisting Carpet Tiles
 Suzanne Alejandre

PreAlgebra, difficulty level 2. For each of the two floors find the total number of degrees that the
sixteen tiles have been rotated.
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Women's Walkway
 Suzanne Alejandre

PreAlgebra, difficulty level 2. How many bricks would it take to cover the full area of the pattern
sample? What's the
area?
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Wondering about Water
 Annie Fetter

PreAlgebra, difficulty level 3. Find the surface area of an Olympicsize ice hockey rink.
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Wraparound Universe
 Jeff Weeks

PreAlgebra, difficulty level 4. Explore the game of tictactoe using a cylindrical tictactoe board.
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