- The Return of the Parallelogram II - Annie Fetter
Geometry, difficulty level 3. Draw a 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 the area of the parallelogram?
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- Running a Mile on a Metric Track - Annie Fetter
Geometry, difficulty level 4. How far out from the rail on a 400 meter track would you have to run to cover 440 yards?
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- Scintillating Similarity - Annie Fetter
Geometry, difficulty level 2. Given a triangle with sides of 3, 4, and 6. What is the perimeter of the smallest triangle that is similar to the first one and has one side with length 12?
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- 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
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
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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- 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 Many Similar Triangles! - Annie Fetter
Geometry, difficulty level 3. Explain how to form pairs of similar triangles given four rods of
specific lengths and any other two rods from the extra supply.
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- A Space Diagonal - Terry Trotter, MATHCOUNTS
Algebra, difficulty level 2. Find the space diagonal of a certain cube in a sequence of cubes.
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- The Spiral on the Can - Ethel Breuche
Algebra, difficulty level 3. By using the Pythagorean theorem, students can find the length of the spiral painted on a can.
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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 Square - Terry Trotter
Algebra, difficulty level 3. A square is drawn on a coordinate plane with vertices P(1, 0), Q(2, 0), R(2, 1) and S(1, 1). A line is drawn from the origin that cuts the square into two sections whose areas are in a ratio of 2:1. What's the equation
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- Spring Garden Planning - Judy Ann Brown
Pre-algebra, difficulty level 4. Find the area as well as the length and width of my fractional garden.
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- The Square and the Line - Leigh Nataro
Trig/Calc, difficulty level 1. Find the equation of the line that will split a unit square into two pieces that have equal areas.
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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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- Squares Inside Squares - Leigh Nataro
Trig/Calc, difficulty level 3. Find the sum of the perimeters of three nesting squares. Imagine that the process of nesting squares continues forever. The sum of the perimeters approaches a finite number. What is that number?
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- Stained Glass Window - Jackson First Year Algebra Class
Elementary, difficulty level 5. Find the size of a stained glass window for my front door.
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- A Stellar Garden - Bill Marthinsen
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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- 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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- Stonybrooke River Bridge - Leigh Nataro
Trig/Calc, difficulty level 2. Based on given information, find the distance across a river.
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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 Supermarket Shelf - Leigh Nataro
Trig/Calc, difficulty level 3. What is the optimal shelf height in the supermarket?
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- The Super Yard XT - Leigh Nataro
Trig/Calc, difficulty level 1. Based on information about the area of a regular polygon-shaped play yard, find the length of one of the walls of the yard.
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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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- 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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- A Triangle's Area - Canadian Open Math Challenge 1999 via Tim Lang
Algebra, difficulty level 3. Find the "b" values of two lines needed to form two congruent triangles of a given area.
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- Triangles, Sines, and Areas - Leigh Nataro
Trig/Calc, difficulty level 3. Show that the area of any triangle is .5*b*c*sin(A).
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- Tricky Triangles - Lisa Lavelle
Elementary, difficulty level 3. Arrange six toothpicks to create special triangles.
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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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- The Unit Circle Triangle - Leigh Nataro
Trig/Calc, difficulty level 2. Find the area of the largest right triangle in the first quadrant of the unit circle.
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- Visiting Friends - Annie Fetter
Geometry, difficulty level 2. Annie and Suzanne live near the same train station. If you are told
how long it takes to walk from each of their houses to the train
station, what can we say about how long it takes to walk at this rate
directly from
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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 Is My Dimension? - Leigh Nataro
Trig/Calc, difficulty level 4. Find the fractal dimension of the Koch curve.
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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 My Angle? - Terry Trotter
Algebra, difficulty level 3. Using concepts of vertical angles and supplementary angles, solve two quadratic expressions to find the measure of a given angle.
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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 21-sided inscribed regular polygon, PQ is a side of a 28-sided incribed regular polygon, and QR is a side of an n-sided inscribed regular polyon, find a possible
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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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- 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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