 The Protean Perimeter  Annie Fetter
Geometry, difficulty level 3. Given isosceles triangle ABC, with AC=AB=5 inches and angle CAB greater than or equal to 60, what's the perimeter of the triangle if all the edgelengths must be integers?
...more>>
 The Puzzling Parallelogram  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 FD?
...more>>
 Quad Query  Annie Fetter
Geometry, difficulty level 2. Given quadrilateral ABCD, with E the midpoint of AB and F the midpoint of AD. The area of FAEC is 13. What's the area of ABCD?
...more>>
 A Quickie Triangle Puzzle  Sasha Sokolsky
Geometry, difficulty level 2. Find the length of the unknown side of this triangle using knowledge of special right triangles.
...more>>
 Rabbit's Run  Lisa Lavelle
Math Fundamentals, difficulty level 1. Help Regina develop options for building her rabbit's run.
...more>>
 Regional Ratios  Annie Fetter
Geometry, difficulty level 2. A regular hexagon and an equilateral triangle have the same perimeter. What's the ratio of their areas?
...more>>
 Returning to Napoleon's River  Annie Fetter
Geometry, difficulty level 3. A soldier stands on the bank of a river and uses his cap to measure its width. How far off will he be if he drops his head even one degree?
...more>>
 The Return of the Parallelogram I  Annie Fetter
Geometry, difficulty level 3. Given parallelogram ABCD, with AB=10, and E on AB and F on CD. If EF is 4, what is the area of ABCD?
...more>>
 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?
...more>>
 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?
...more>>
 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?
...more>>
 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?
...more>>
 Shapes Rock  Judy Ann Brown
PreAlgebra, difficulty level 3. Find the number of diagonals in a polygon of 40 sides.
...more>>
 Shine On Harvest Moon  Judy Ann Brown
PreAlgebra, difficulty level 2. Find the area of the largest circle that can be cut from a nineinch by twelveinch sheet of paper.
...more>>
 Ships Ahoy!  Annie Fetter
Geometry, difficulty level 2. Examine some methods Thales might have used to measure the distance to
ships at sea.
...more>>
 Shortcut Savings  Suzanne Alejandre
PreAlgebra, difficulty level 2. Find a rule to tell how much distance I will save when I take the shortcut.
...more>>
 The Shortest Possible Side  Annie Fetter
Geometry, difficulty level 2. Find the shortest possible side length of a triangle with a given
perimeter.
...more>>
 Similar Perimeter  Annie Fetter
Geometry, difficulty level 2. Find the coordinates of the vertices of a triangle similar to the
given triangle with the designated perimeter.
...more>>
 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.
...more>>
 Snail's Trail  Annie Fetter, Lillian Ray
Geometry, difficulty level 2. What should be the dimensions of the smallest piece of my "Snail's
Trail" quilt?
...more>>
 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?
...more>>
 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.
...more>>
 A Space Diagonal  Terry Trotter, MATHCOUNTS
Algebra, difficulty level 2. Find the space diagonal of a certain cube in a sequence of cubes.
...more>>
 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.
...more>>
 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?
...more>>
 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 of
...more>>
 Spring Garden Planning  Judy Ann Brown
PreAlgebra, difficulty level 4. Find the area as well as the length and width of my fractional garden.
...more>>
 Spring Up, Fall Back  Annie Fetter
Geometry, difficulty level 2. Help build a new rail for these solar panels so that they can be set
at three different angles.
...more>>
 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.
...more>>
 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.
...more>>
 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?
...more>>
 Stained Glass Window  Jackson First Year Algebra Class
Elementary, difficulty level 5. Find the size of a stained glass window for my front door.
...more>>
 Steam Up!  Annie Fetter
Geometry, difficulty level 3. Calculating the grade of an incline and the length of a train.
...more>>
 A Stellar Garden  Bill Marthinsen
PreAlgebra, difficulty level 3. Martha Stewart wants to rebuild her ugly garden. She needs help calculating the areas in the new garden.
...more>>
 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?
...more>>
 Stonybrooke River Bridge  Leigh Nataro
Trig/Calc, difficulty level 2. Based on given information, find the distance across a river.
...more>>
 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?
...more>>
 The Supermarket Shelf  Leigh Nataro
Trig/Calc, difficulty level 3. What is the optimal shelf height in the supermarket?
...more>>
 The Super Yard XT  Leigh Nataro
Trig/Calc, difficulty level 1. Based on information about the area of a regular polygonshaped play yard, find the length of one of the walls of the yard.
...more>>
 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?
...more>>
 Talladega Afternoons  Annie Fetter
Geometry, difficulty level 1. Compare the corner banking of a track to the steepness of the roof of
a house.
...more>>
 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.
...more>>
 Tied in Knots  Annie Fetter
Geometry, difficulty level 2. How many triangles can be made from the knotted rope?
...more>>
 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.
...more>>
 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?
...more>>
 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.
...more>>
 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.
...more>>
 Triangles, Sines, and Areas  Leigh Nataro
Trig/Calc, difficulty level 3. Show that the area of any triangle is .5*b*c*sin(A).
...more>>
 Tricky Triangles  Lisa Lavelle
Elementary, difficulty level 3. Arrange six toothpicks to create special triangles.
...more>>
 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.
...more>>
 
