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Problems
Geometry
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Browse all Geometry Problems of the Week
Participation in the Geometry Problems of the
Week allows teachers and students to address the
NCTM
Problem Solving Standard for Grades 9-12, enabling students to
build new mathematical knowledge through problem solving; solve problems
that arise in mathematics and in other contexts; apply and adapt a
variety of appropriate strategies to solve problems; and monitor and
reflect on the process of mathematical problem solving.
For background information elsewhere on our site, explore the
High School Geometry
area of the Ask Dr. Math archives. To find relevant
sites on the Web, browse and search
Geometry
in our Internet Mathematics Library.
Access to these problems requires a Membership.
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Coordinated Triangle?
- Annie Fetter
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Geometry, difficulty level 3. Triangle ABC has an area of 24 units^2. Point A is at (6,0); point B is at (10,0). Where can point C be? What if the triangle is
isosceles?
... more>>
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Counting Squares
- Annie Fetter
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Geometry, difficulty level 2. Count the total number of squares in the given diagram.
... more>>
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Cutting Corners
- Annie Fetter
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Geometry, difficulty level 1. Some election signs must have corners cut off them to comply with
local election rules.
... more>>
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Dendrochronology
- Annie Fetter
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Geometry, difficulty level 2. Figure out about how old a large yellow birch is, given its diameter.
... more>>
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Descartes' Triangle?
- Annie Fetter
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Geometry, difficulty level 3. Two vertices of a triangle are located at (0,6) and (0,12). If the area of the triangle is 12 square units, where can the third vertex be? What if the triangle is also isosceles?
... more>>
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Diagonal Dilemma
- Karen Cohen
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Geometry, difficulty level 1. What is the area of the square ABCD that has a diagonal of length 12 cm?
... more>>
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The Diagonal Triangle
- Annie Fetter
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Geometry, difficulty level 1. A triangle is formed by connecting opposite vertices of a figure formed by two squares. Find the area of the triangle.
... more>>
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Different Views
- Annie Fetter
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Geometry, difficulty level 3. Given a front, top, and side view of an object, find the volume of that object.
... more>>
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Dilating a Quadrilateral
- Annie Fetter
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Geometry, difficulty level 3. Given two similar quadrilaterals on a coordinate grid, determine the ratio and center of dilation.
... more>>
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Divided Rectangle
- Annie Fetter
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Geometry, difficulty level 1. A rectangle is divided into four rectangles with areas 45, 25, 15, and x. Find x.
... more>>
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Drawing a Kite Plan
- Annie Fetter
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Geometry, difficulty level 3. Given a picture of a kite plan, figure out the radius of the circle that creates the curved section.
... more>>
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Drawing Out a Decagon
- Annie Fetter
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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>>
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Dueling Spheres
- Annie Fetter
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Geometry, difficulty level 2. You're given two spheres with centers 14 cm apart. The circumference
of the circle where they intersect is 24 pi cm, and the radius of one
sphere is 13 cm. What's the radius of the other sphere?
... more>>
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Eight Sticks and Zero Triangles
- Annie Fetter
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Geometry, difficulty level 3. Help Imeir and Dat answer this question about sticks of integer
length that cannot make triangles.
... more>>
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Eminen
- Annie Fetter
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Geometry, difficulty level 3. Figure out what size squares will tile a rectangle.
... more>>
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Equal Area & Congruence
- Annie Fetter
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Geometry, difficulty level 2. If two triangles are congruent, they have the same area. Is the converse true?
... more>>
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Equilateral Triangle and Square Ratio
- Dale Pearson
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Geometry, difficulty level 3. A square with side length s is inscribed in an equilateral triangle of
side length t. Find the ratio t/s.
... more>>
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Equilateral Triangle Areas
- Annie Fetter & Steve Weimar (extra)
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Geometry, difficulty level 3. If two equilateral triangles have edgelengths of 9 cubits and 12
cubits, what's the edgelength of the equilateral triangle whose area
is equal to the sum of the areas of the other two?
... more>>
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Equilateral Triangles and Circles
- Annie Fetter
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Geometry, difficulty level 2. Two vertices of an equilateral triangle are on the diameter of a circle whose area is 49 pi. The other vertex is on the circumference of the circle. What's the largest possible area of the triangle?
... more>>
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Examining an Octagon
- Annie Fetter
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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>>
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Explanation Only!
- Annie Fetter
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Geometry, difficulty level 4. Prove that x/(1-x) = 1/x in the given picture.
... more>>
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Exploding Shapes
- Annie Fetter
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Geometry, difficulty level 2. How will Clarissa finish her dilation?
... more>>
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Extending the Enneagon
- Annie Fetter
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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>>
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Extending the Signals
- Lisa Lavelle
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Trig/Calc, difficulty level 1. Determine how far Erin needs to "rotate" to signal Joey at his cousin's house.
... more>>
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Field of View
- Annie Fetter
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Geometry, difficulty level 2. Figure out the field of view for two different pairs of binoculars.
... more>>
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Filling the Hot Tub
- Annie Fetter and Steve Risberg
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Geometry, difficulty level 3. Given the dimensions of a hot tub and its submerged wood-burning
stove, figure out how long it will take to fill the tub using a
garden hose.
... more>>
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Finding a Supplement
- Terry Trotter & Annie Fetter
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Geometry, difficulty level 1. Two lines, AB and CD, intersect at point E. Angles AED and CEB have measures that can be expressed as 2x^2 + 3x + 15 and 3x^2 + x - 20. Find all of the possible measures of angle BED.
... more>>
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Finding CE
- Annie Fetter
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Geometry, difficulty level 4. Side AB of triangle ABC has a length of 8 inches. Line DEF is drawn
parallel to AB so that D is on segment AC and E is on segment BC. Line
AE extended bisects angle FEC. If DE has a length of 5 inches, what's
the length of CE?
... more>>
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Finding FAB
- Annie Fetter
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Geometry, difficulty level 2. The measure of one angle in the given picture is x. Using your
knowledge of rhombii and triangles (and other things!), find the
measure of another angle.
... more>>
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Finding Fireworks
- Annie Fetter
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Geometry, difficulty level 2. Do Nasheed and Graciella have enough information to figure out where the
fireworks show is?
... more>>
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Finding the Base of a Trapezoid
- Annie Fetter
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Geometry, difficulty level 3. Given trapezoid ABCD, with AD one base and BC the other and a 60 degree angle at CDA. If CD is 26sqrt3/3 meters, BC is 7 meters, and the area of the trapezoid is 130 square meters, what's the length of AD?
... more>>
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Finding the Side of a Parallelogram
- Annie Fetter
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Geometry, difficulty level 3. In parallelogram ABCD, the bisector of angle ABC intersects AD at point P. PD is 5, BP is 6, and CP is 6. What's AB?
... more>>
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Finding the Volume of a Box
- Annie Fetter
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Geometry, difficulty level 2. If the areas of the top and front of a box are 252 and 105 square inches, respectively, and the surface area of the box is 834 square inches, what's the volume of the box?
... more>>
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Find the Area of This Square
- Annie Fetter
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Geometry, difficulty level 2. Given a square split into four pieces, one with an area of 35 and the other with an area of 8, find the area of the whole square.
... more>>
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Find the Largest Equilateral Triangle
- Annie Fetter
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Geometry, difficulty level 3. Two vertices of an equilateral triangle lie on a diameter of a circle whose area is 36pi cm^2, and the third vertex lies on the circle. What is the largest possible area of the triangle?
... more>>
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Find the Perimeter
- Annie Fetter
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Geometry, difficulty level 3. In the given picture, DB and DC are both 20 inches. What's the perimeter of triangle FDG?
... more>>
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Find the Volume of a Box
- Annie Fetter
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Geometry, difficulty level 2. Given the surface area of three sides, find the dimensions and volume of a rectangular box.
... more>>
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Find This Angle
- Annie Fetter
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Geometry, difficulty level 3. Given triangle ABC, where E is on AB and DB is perpendicular to AE. AC = BC, angle ACB is twice the measure of angle CBD, and angle DBE = 90 degrees. What is angle CBD?
... more>>
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Fitting In
- Annie Fetter
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Geometry, difficulty level 3. Figure out which peg takes up a larger percentage of the corresponding
hole.
... more>>
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Fix This Picture
- Annie Fetter
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Geometry, difficulty level 2. Figure out what's wrong with this picture that includes a circle and a rhombus.
... more>>
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Flying High
- Annie Fetter
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Geometry, difficulty level 1. Figure out which of two planes is gaining altitude more quickly.
... more>>
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Folding a Piece of Paper in Thirds
- Annie Fetter
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Geometry, difficulty level 3. Show that the given folds mark a piece of paper exactly in thirds.
... more>>
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Folding a Rectangle
- Annie Fetter
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Geometry, difficulty level 3. Fold a 6-inch by 8-inch piece of paper so that the opposite corners
meet. How long is the fold?
... more>>
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The Folding Ruler
- Annie Fetter
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Geometry, difficulty level 2. Describe all of the possible triangles that can be made with the full length of a 6 foot long folding wooden ruler.
... more>>
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Four Point Puzzle
- Annie Fetter
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Geometry, difficulty level 3. The vertices of quadrilateral ABCD are at the points A:(1,2),
B:(2,-2), C:(-5,-4), and D(-6,0). What's the most specific name you
can give to this quadrilateral?
... more>>
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Framed!
- Annie Fetter
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Geometry, difficulty level 3. Given a triangular painting with dimensions 20 x 14 x 10, and three different ways you could frame it, which frame will take the least amount of material?
... more>>
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A Gardening Puzzle
- Annie Fetter
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Geometry, difficulty level 2. If a rectangular garden were 2 feet wider and 3 feet longer, it would be 64 square feet larger. If it were 3 feet wider and 2 feet longer, it would be 68 square feet larger. What are the dimensions of the garden?
... more>>
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Geoboard Gymnastics
- Annie Fetter
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Geometry, difficulty level 3. Find squares with different areas on a geoboard.
... more>>
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