TOPICS
This page:
all geometry
About Levels
of Difficulty
Geometry
lines/angles
triangles
quadrilaterals
polygons
circles
perimeter, area,
volume
similar/congruent
right triangles
transform/symmetry
construction/locus
coordinate geometry
modeling/applications
Browse all
Geometry
Problems
Geometry
Home
About the
PoW Library

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 912, 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.

Added Areas
 Annie Fetter

Geometry, difficulty level 1. A circle and an isosceles triangle are inscribed in a square. If the areas of the three figures added together is 28 square units, what's the edgelength of the square?
... more>>

All Around the World
 Terry Trotter & Annie Fetter

Geometry, difficulty level 2. If a wire wrapped around the equator of the Earth is lengthened by 100 meters, how far above the surface of the Earth would the wire now be if lifted off the surface an equal distance all the way around?
... more>>

Analyzing Angles
 Annie Fetter

Geometry, difficulty level 2. Given some information about angles in a picture, figure out some of
the angle measures.
... more>>

Another Ambiguous Angle?
 Annie Fetter

Geometry, difficulty level 3. Given isosceles triangle ABC, with BE perpendicular to AD. If angle ACB is x, what is angle CBE?
... more>>

Ants Marching
 Annie Fetter

Geometry, difficulty level 2. Traveling along the edges of a cross section of the cube, find the
length of the shortest possible path from one corner of a cube to the
opposite corner, as well as the longest possible path between the same
corners.
... more>>

The Apprehendable Angle
 Annie Fetter

Geometry, difficulty level 2. Triangle ABC is isosceles with a vertex angle (at the top) of 50 degrees. If D is on AC, E is on BC, and AD = BE, what is the measure of angle ADE?
... more>>

Approximating Pi
 Annie Fetter

Geometry, difficulty level 3. Approximate the value of pi using polygons instead of a circle.
... more>>

Arc to Area
 Annie Fetter

Geometry, difficulty level 4. Given an arc with a measure of 40 degrees whose endpoints are at (1,5) and (5,3), find the area of the circle that contains the arc.
... more>>

Arda and Brooke's Catapult
 Annie Fetter

Geometry, difficulty level 2. Does Arda's method for measuring the distance across the river really
work?
... more>>

Area of a Rectangle
 Annie Fetter

Geometry, difficulty level 2. Given rectangle ABCD with point E on CD. AE is 3, BE is 4, and AE is perpendicular to BE. What's the area of ABCD?
... more>>

Area of a Rhombus
 Annie Fetter

Geometry, difficulty level 2. Find the area of a rhombus, given one angle measure and the length of
the longer diagonal.
... more>>

Arranging Rectangles
 Annie Fetter

Geometry, difficulty level 3. Help Kasim decide if his arrangement of rectangles could ever form a square.
... more>>

As Far as the Eye Can See
 Annie Fetter

Geometry, difficulty level 4. If I'm 5'10" tall, can I see the entire length of Lake Memphramagog, which is about 23 miles long?
... more>>

Assessing Seismic Risk
 Craig Foster and Annie Fetter

Geometry, difficulty level 3. Figure out how likely it would be for an earthquake to occur within
certain distances of a building.
... more>>

Beach Boys
 Steve Risberg

Geometry, difficulty level 3. Help Skip and Gil find the height of the cruise ship.
... more>>

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>>

Bouncing Billiards
 Annie Fetter

Geometry, difficulty level 1. Help Maria decide the angle that will sink her cue shot after four
bounces.
... more>>

Boxing Up Harry's Broom
 Annie Fetter

Geometry, difficulty level 1. Help Harry find the right size box for his broom.
... more>>

Broken Pottery
 Annie Fetter

Geometry, difficulty level 2. Explain how to find the center of this sherd.
... more>>

Building a Rain Gauge
 Annie Fetter

Geometry, difficulty level 3. Given the depth of the water in a bottle, figure out how much rain really fell, considering that the opening of the bottle is much smaller than the main part.
... 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>>

Building a Vaulted Ceiling
 Annie Fetter

Geometry, difficulty level 4. An eyebrow window is a 15inchdeep slice off an 8.5foot circle. How wide will the base of the window be?
... more>>

Building Bookshelves
 Steve Weimar

Geometry, difficulty level 2. Merriem and Emmanuel's new bookshelf hits the ceiling when they try to
put it in place. Explain why, and help them figure out how much to
cut off the bottom so that it will fit.
... 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>>

Buying Paint and Shingles
 Annie Fetter

Geometry, difficulty level 2. Figure out how many gallons of paint and how many bundles of shingles I need to buy to finish my new shed.
... more>>

Calculating String Length
 Annie Fetter

Geometry, difficulty level 2. Given the archery targets of two competitors, figure out which one has the shortest 'string length'.
... more>>

A Carpenter's Trisection
 Annie Fetter

Geometry, difficulty level 3. Explain whether or not the given method of trisecting an angle, using only a carpenter's square, really works.
... more>>

Circle Derby
 Terry Trotter

Geometry, difficulty level 2. Determine which dot has the small angle to go and which has the
shortest distance to go in this race around a circle.
... more>>

A Circle Inscribed in an Isosceles Triangle
 Ilmar Vitsut

Geometry, difficulty level 4. Find the radius of a circle inscribed in an isosceles triangle with sides 12, 12, and 8.
... more>>

Circle Intersections
 Annie Fetter

Geometry, difficulty level 2. What is the maximum number of times that six circles of the same size could intersect?
... more>>

Circles and Tangents
 Annie Fetter

Geometry, difficulty level 3. AOD is a diameter of circle O. B is any point on the circle. At B, a tangent is drawn to the circle. From the center, O, a line is drawn parallel to AB, meeting the tangent at P. Prove that PD is tangent to
the circle.
... more>>

Circumnavigating Circles
 Annie Fetter

Geometry, difficulty level 3. The radii of two wheels are 10 vershoks and 5 vershoks and their centers are 30 vershoks apart. A belt goes around both of the wheels, crisscrossing between the two centers to form two internal tangents. What's the length of the belt?
... more>>

Clever Cuts
 Annie Fetter

Geometry, difficulty level 2. Find three different ways to cut a hexagonal cake into six congruent
pieces.
... more>>

Comparing the Areas of Two Squares
 Annie Fetter

Geometry, difficulty level 3. Given two squares, one with the diameter of a circle as an edge, the
other inscribed in the circle. How do the areas of the squares
compare?
... more>>

Congruence and Area
 Annie Fetter

Geometry, difficulty level 3. "If two triangles have the same area, then they are congruent." Is this a true statement?
... more>>

Congruent Chords and Circles
 Annie Fetter

Geometry, difficulty level 4. Prove that two congruent chords in a circle are equal distances from the center of the circle.
... more>>

Congruent Chords
 Annie Fetter

Geometry, difficulty level 3. Two congruent circles are drawn, and four congruent chords are drawn, two in each circle, all perpendicular to the diameter through both circles. The distance between the two furthest chords is 20, and the distance between two chords of the same circle is 8. What's the area of one of the circles?
... more>>

Congruent Rectangles
 Annie Fetter

Geometry, difficulty level 1. Seven congruent rectangles are arranged to form a larger rectangle. If the area of the large rectangle is 756 units^2, what's the perimeter of the large rectangle?
... more>>

Congruent Rectangles Help
 Annie Fetter

Geometry, difficulty level 2. Find some possible areas for the large rectangle shown in the
given picture.
... more>>

Constructing a Tangent
 Annie Fetter

Geometry, difficulty level 3. Explain why this construction of a tangent works.
... 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>>

Constructing the Great Pyramid
 Annie Fetter & Suzanne Alejandre

Geometry, difficulty level 2. Figure out if the instructions provided will result in a scale
model of the Great Pyramid of Giza.
... more>>

The Coordinated Quadrilateral
 Annie Fetter

Geometry, difficulty level 3. A quadrilateral has vertices at (3,6), (1,2), (7,4), and (5,4). What kind of quadrilateral is it?
... more>>
Page: 1
2
3
4
5
6
[next>]
