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 geometry in the plane
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Pre-Algebra
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Pre-Algebra
Problems
Pre-Algebra
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Geometry in the Plane
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Problems in this category require students to describe, classify, and understand the relations that exist among two-dimensional 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
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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 6-8
Access to these problems requires a Membership.
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3-D Vision
- Annie Fetter
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, difficulty level 3. Plan a garden so as to maximize the area surrounded by a 36-yard fence.
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Building on Water
- Judy Ann Brown
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, difficulty level 3. Chamique wants to know the probability of hitting a bull's-eye with a randomly shot arrow.
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Coloring a Hexagon
- Ranjan Rohatgi, Spencer Koerner, Suzanne Alejandre
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, difficulty level 2. Graph six points and find the area of the resulting hexagon.
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Graphs
- Suzanne Alejandre, Annie Fetter
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Pre-Algebra, 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 y-axes.
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How Fast Is a Minute?
- Suzanne Alejandre
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, difficulty level 3. Find the total cost of purchasing tiles for my office.
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Partial Area
- Judy Ann Brown
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, 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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Picture-Perfect Geometry
- Judy Ann Brown
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Pre-Algebra, difficulty level 2. Graph four points and name the figure that you have drawn.
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Pizza Pie
- Judy Ann Brown
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, difficulty level 2. Find the area of the largest circle that can be cut from a nine-inch by twelve-inch sheet of paper.
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Shortcut Savings
- Suzanne Alejandre
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, difficulty level 3. Identify the types of symmetries of each of three patterns.
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Tiling Triangles
- Suzanne Alejandre
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Pre-Algebra, 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
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Pre-Algebra, difficulty level 3. A tree breaks three-eighths 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
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, difficulty level 3. Find the surface area of an Olympic-size ice hockey rink.
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Wraparound Universe
- Jeff Weeks
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Pre-Algebra, difficulty level 4. Explore the game of tic-tac-toe using a cylindrical tic-tac-toe board.
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