 Seven Congruent Rectangles  Annie Fetter
Geometry, difficulty level 2. Seven congruent rectangles are arranged to form a larger rectangle. If the area of the large rectangle is 336 units^2, what's the perimeter of the large rectangle?
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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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 Sighting in a Rifle  Annie Fetter
Geometry, difficulty level 3. Analyze the given target of four shots, and tell me how far to move the scope on my rifle so that the group of shots will be centered around the bull'seye.
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 Slicing a Cube  Annie Fetter
Geometry, difficulty level 3. Given a cube with a surface area of 54 cm^2, find the perimeter of the square cross section and that of the largest rectangular cross section of that cube.
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 Snow Removal  Annie Fetter
Geometry, difficulty level 4. How many times would the snow in the Math Forum parking lot fill my office? How many pounds does all that snow weigh?
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 So, What Do You Know About Tangents?  Annie Fetter
Geometry, difficulty level 3. AB and CB are tangents to a circle, with A and C on the circle and B their intersection. D is a point on the minor arc AC, and a tangent is drawn at D, which intersects the AB at E and CB at F. What is the perimeter of EFB?
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 The Speed Skating Oval  Annie Fetter
Geometry, difficulty level 2. Find the radii of the turns of a 400 meter speed skating oval.
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 Splitting a Hexagon  Annie Fetter
Geometry, difficulty level 2. Split a regular hexagon into three identical parts. What shape is each part? Split a regular hexagon into six identical parts, at least two different ways. What shapes are you r pieces? Split a regular hexagon into six identical
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 Splitting a Parallelogram  Annie Fetter
Geometry, difficulty level 3. Draw parallelogram ABCD with AB = 10. Draw EF with E between A and B and F between C and D such that EF divides the area of ABCD in half. If EF = 4, what is FD?
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 Splitting a Plane  Annie Fetter
Geometry, difficulty level 3. What's the greatest number of regions into which you can split a plane using six lines?
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 Splitting Space  Annie Fetter
Geometry, difficulty level 4. What's the greatest number of regions into which you can divide space using four planes?
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 The Square Cross Section of a Tetrahedron  Annie Fetter
Geometry, difficulty level 3. Given a regular tetrahedron with an edgelength of 10, find the area and perimeter of the square cross section and how to get that cross section.
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 Square in a Right Triangle  Annie Fetter
Geometry, difficulty level 3. In the given picture, square DEFG is inscribed in a right triangle ABC (with right angle at B) with DG on AC, E on AB, and F on BC. If AD is 14 and GC is 29, what's the area of the square?
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 St. George's Banner  Annie Fetter
Geometry, difficulty level 2. Find out how wide the cross on this flag needs to be in order for the red and white regions to have the same area. If the flag is x feet by y feet, how wide is the red stripe?
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 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?
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 The Subtending Chord  Annie Fetter
Geometry, difficulty level 3. A chord of a circle is the hypotenuse of an isosceles right triangle whose legs are radii of the circle. The length of the chord is 8 times the square root of 2. What is the length of the minor arc subtended by the chord?
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 The Sun vs. the Earth  Annie Fetter
Geometry, difficulty level 1. Would one million Earths really fit inside the sun?
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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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 Taking Pictures of the Earth  Annie Fetter
Geometry, difficulty level 4. If you wanted to go out into space and take a picture of the earth, how far from the earth would you have to go to make sure that you got 1/4 of the equator in your picture? How about 1/3?
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 Tangrams  Abram Falk
Geometry, difficulty level 3. Explain which triangles in a tangram are congruent to each other and what the area is of each piece.
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 Tangrams and Perimeter  Annie Fetter
Geometry, difficulty level 2. What are the perimeters of the pieces of a tangram?
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 Tangrams, Congruent Triangles, and Area  Annie Fetter
Geometry, difficulty level 3. Tell me which pieces of a tangram are congruent, and tell me the area of each of the pieces.
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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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 Transforming a Triangle  Annie Fetter
Geometry, difficulty level 1. Given two triangles on a coordinate plane, find a pair of transformations that will map the first triangle onto the second triangle.
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 A Trapezoidal Garden  Annie Fetter
Geometry, difficulty level 2. Given trapezoid ABCD, with E on AD and F on BC and EF parallel to AB. If AE is 3/4 of ED, and BC is 14 feet, how long is FC? How does the area of DCFE compare to the area of EFBA?
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 Triangles and String  Annie Fetter and Steve Risberg
Geometry, difficulty level 2. Given a loop of string 12" long, find all possible triangles of integer side lengths that it can form, and explain whether they are scalene, isosceles, or equilateral, as well as acute, right, or obtuse.
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 Triangles, Area, and Congruence  Annie Fetter
Geometry, difficulty level 2. If two triangles have equal area, does that mean that they are congruent?
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 Triangle Transformation  Annie Fetter
Geometry, difficulty level 3. Given triangles ABC and DEF on the coordinate plane and a list of transformations, explain how to map ABC onto DEF in only two steps.
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 Triple Tango  Annie Fetter
Geometry, difficulty level 1. Sort six triangles into three pairs so that the two triangles in each pair can be put together to form a larger triangle without overlapping.
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 Two Houses and a Carrier Pigeon  Annie Fetter
Geometry, difficulty level 3. One house is 300 yards from a highway. 1200 yards down the highway is the driveway to another house, 600 yards from the highway, on the same side of the road. What is the shortest distance between the two houses if you go
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 Two Times Two Angles  Annie Fetter
Geometry, difficulty level 3. The measures of two angles are in the ratio 5:3. The measure of the larger angle is 30 greater than half the difference of the angles. Find the measure of each angle.
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 Unravelling the Mysteries of the Universe  Annie Fetter
Geometry, difficulty level 2. How many Earths can fit in Uranus?
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 Up Periscope!  Annie Fetter
Geometry, difficulty level 2. Given a diagram of a broken submarine periscope, explain which angles need to be equal in order to for the image to reach the eyepiece.
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 Valley Springs Snow Cream  Kelly Crisp
PreAlgebra, difficulty level 3. Compare the volume of a sphere, cone, and cylinder using ice cream.
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 Waiting for Hot Water  Annie Fetter
Geometry, difficulty level 2. If a water pipe is 1/2" in diameter, the faucet is about 35 feet from the hot water tank, and the faucet runs at 3 gallons per minute, how long will it take the hot water in the tank to reach the faucet?
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 Walking Fast  Annie Fetter
Geometry, difficulty level 2. A woman with a 28" inseam takes 5 steps for every 4 steps I take. I have a 34" inseam and cover 20 yards in 20 steps. Am I covering more ground because my legs are longer, or because my legs form a larger angle with each
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 What Do We Know About Tangents?  Annie Fetter
Geometry, difficulty level 2. Given two externally tangent congruent circles, construct a segment from the center of one circle tangent to the other circle. If the length of this segment is 10, what's the radius of the circles?
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 What's My Angle?  Annie Fetter
Geometry, difficulty level 2. Given line AE, point C between A and E, ray CB perpendicular to line AE, and point D on the same side of AE as point B. If CD equals DE and angle CDE is x degrees, what is the angle measure of angle BCD?
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 What's This Polygon?  Annie Fetter
Geometry, difficulty level 4. Triangle PQR is inscribed in a circle. If PR is a side of a 21sided inscribed regular polygon, PQ is a side of a 28sided incribed regular polygon, and QR is a side of an nsided inscribed regular polyon, find a possible
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 Where's J?  Annie Fetter
Geometry, difficulty level 2. Given an isosceles triangle with one base vertex (O) on the origin, the other base vertex (J) on the positive xaxis, and the top vertex at the point (e,f), find the coordinates of J.
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 Which Pizza?  Annie Fetter
Geometry, difficulty level 2. Which is a better deal  a 16" diameter pizza for $11 or a 10" diameter pizza for $7?
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 Who Wants to be an Archery Champion?  Annie Fetter
Geometry, difficulty level 2. To determine the winner, calculate the "string length" for each of two archery rounds.
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 Winning at Biathlon  Annie Fetter
Geometry, difficulty level 3. Figure out which of two fictional biathletes will win a race.
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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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 World Series Snafu?  Annie Fetter
Geometry, difficulty level 2. Determine what's wrong with the "official" dimensions of "home plate" in baseball.
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