 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?
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 Adventure Airlines  Leigh Nataro
Trig/Calc, difficulty level 1. How far from the airport does the plane need to begin its descent?
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 Aim at This Target!  Annie Fetter
Geometry, difficulty level 4. Figure out the areas of different parts of this target, and the relation between the different areas. Can you explain this relation?
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 All Wet  Linda Benton
Algebra, difficulty level 3. Solve simultaneous equations, find area, and use the Pythagorean theorem and percentages to find the spraying distance needed for a circular sprinkler in a rectangular yard.
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 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?
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 Another Problematic Pizza  Leigh Nataro
Trig/Calc, difficulty level 3. Find the area of a triangular piece of pizza.
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 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?
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 Approximating the Circumference and Area of a Circle  Annie Fetter
Geometry, difficulty level 2. Take a circle and circumscribe a square and inscribe a square. Construct a square between the other two squares, and compare the area and the perimeter of the middle square with the area and circumference of the circle.
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 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.
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 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.
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 Around the Corner  Louis Holmes
Trig/Calc, difficulty level 4. A girder must be carried along a corridor that has a 90degree turn at the end. How wide must the corridor be in order for the girder to fit around the corner?
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 Arranging Six Squares  Annie Fetter
Geometry, difficulty level 3. How many ways can you arrange six squares in the plane so that they all share an edge with at least one other square? How many of these configurations could be folded up to form a cube?
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 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?
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 Beach Boys  Steve Risberg
Geometry, difficulty level 3. Help Skip and Gil find the height of the cruise ship.
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 Boxing Up Harry's Broom  Annie Fetter
Geometry, difficulty level 1. Help Harry find the right size box for his broom.
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 Building a Bridge Across a Chasm  Annie Fetter
Geometry, difficulty level 2. So they're standing on the edge of this chasm. It isn't really that far across, but they need to find a log or tie together enough rope to reach a tree on the other side. So they mark a spot on the edge of the chasm directly
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 Building a Dog Enclosure  Annie Fetter
Geometry, difficulty level 3. Two people are arguing about whether three sections of fencing 6, 8, and 10 feet long will enclose more or less area than three sections 6, 8, and 12 feet long.
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 Building a Sandbox  Leigh Nataro
Trig/Calc, difficulty level 3. Find the maximum area for a triangularshaped sandbox.
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 Building Boxes  Leigh Nataro
Trig/Calc, difficulty level 2. Find the maximum volume of a rectangular prism constructed from an 8.5inch by 11inch piece of paper.
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 Building Bridges  Leigh Nataro
Trig/Calc, difficulty level 3. Given some dimensions, find the length of a cable that lies along the diagonal of a bridge.
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 Building Fences  Judy Ann Brown
PreAlgebra, difficulty level 3. Plan a garden so as to maximize the area surrounded by a 36yard fence.
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 Building on Water  Judy Ann Brown
PreAlgebra, difficulty level 4. Find the area of a circular pond not covered by a rectangular building.
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 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?
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 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'.
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 Canadian Soccer  Judy Ann Brown
PreAlgebra, difficulty level 2. Find the distance a player runs to complete three "Double V" laps.
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 Can You Prove It?  Leigh Nataro
Trig/Calc, difficulty level 3. Prove that the square root of 2 is irrational, and explain how to use a straightedge and compass to construct a segment that is the square root of 2 in length.
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 Center Coordinates  Leigh Nataro
Trig/Calc, difficulty level 2. Find the coordinates of the center of a circle circumscribed around a triangle.
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 The Center of Gravity of a Quadrilateral  Annie Fetter
Geometry, difficulty level 3. Find the center of gravity of a quadrilateral.
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 Checking a Building Foundation for Square  Annie Fetter
Geometry, difficulty level 2. How can you determine whether a rectangle is square when all you have is string and a tape measure?
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 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.
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 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.
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 Clever Cuts  Annie Fetter
Geometry, difficulty level 2. Find three different ways to cut a hexagonal cake into six congruent
pieces.
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 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?
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 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.
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 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?
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 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.
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 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?
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 Coordinated Triangle?  Annie Fetter
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?
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 Coordinateville  Leigh Nataro
Trig/Calc, difficulty level 1. Find the angle of intersection of two roads based on given information.
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 The Corner Banking of the Daytona Speedway  Annie Fetter
Geometry, difficulty level 2. Compare the corner banking at the Daytona Speedway, which is 31 degrees, with the roof on the house and garage that I helped build.
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 Coverage  Larry Sue
Discrete Math, difficulty level 1. This classic problem asks whether the given shape covers the given grid.
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 Descartes' Triangle?  Annie Fetter
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?
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 Diagonal Dilemma  Karen Cohen
Geometry, difficulty level 1. What is the area of the square ABCD that has a diagonal of length 12 cm?
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 Diego's Building Block  Terry Trotter
Algebra, difficulty level 3. Find the surface area of a rectangular prism, given the volume and information about the dimensions.
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 Divided Rectangle  Annie Fetter
Geometry, difficulty level 1. A rectangle is divided into four rectangles with areas 45, 25, 15, and x. Find x.
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 Don't Be Late for Dinner  Leigh Nataro
Trig/Calc, difficulty level 2. Based on given distances, determine whether Susy will be late getting home for dinner.
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 Drawing a Kite Plan  Annie Fetter
Geometry, difficulty level 3. Given a picture of a kite plan, figure out the radius of the circle that creates the curved section.
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 Drawing Out a Decagon  Annie Fetter
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?
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 Dueling Spheres  Annie Fetter
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?
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 Eight Sticks and Zero Triangles  Annie Fetter
Geometry, difficulty level 3. Help Imeir and Dat answer this question about sticks of integer
length that cannot make triangles.
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