Questions 1-15 are worth 4 points each. Questions 16-19 are worth 5 points each.
Find the perimeter and area of each shape.
Find the radius, diameter, circumference, and area.
Find the volume and surface area.
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16) |
Is it possible to draw a triangle with side lengths 5, 2, and 8? If so, draw one. If not, explain why not. |
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17) |
How many squares are there on a chessboard? (Hint: There are more than 64.) |
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18) |
In a certain garden there are 10 trees planted in 5 rows with 4 trees in each row. How is this possible? (Hint: This garden contains no right angles.) |
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| 19) |
A certain theater is 60 feet long, 30 feet wide, and 20 feet tall. If a fly flew in a straight line from one corner to the opposite corner, how far did it fly?
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| 20) |
Garfield's Proof
A few years before being elected the 20th president of the United States, James Garfield produced an original proof of the Pythagorean Theorem. Start with a rectangle that has been cut in half, forming two right triangles with side lengths a, b, c.
  
Rotate one of the triangles 90 degrees to create a trapezoid. The logic of the proof is that the area of the trapezoid should equal the area of the three triangles contained within it. Use the formulas for area of a trapezoid and area of a triangle to set up this equation. Then expand the left side of the equation and simplify.
Area of Trapezoid = Area of ABC + Area of ADE + Area of ABE.
Show how this proves the Pythagorean Theorem. (10 points) |
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| 21) |
Seven Bridges
In the 18th century, in the German town of Konigsberg, a popular pastime was to walk across its seven bridges.
Is it possible to walk so that you cross each bridge once and only once. If so, how? If not, why not? (10 points) |
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- BONUS QUESTION: The Unexplained Hole
Below, the same four parts are assembled in two different arrangements.
Out of nowhere a hole appears in the second arrangement. How can this be? (10 points)