Geometry Problem of the Week: Sept. - Dec. 1996
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- Sept. 2-6 - Divided Rectangle: A rectangle is divided into four rectangles with areas 45, 25, 15, and x. Find x.
- Sept. 9-13 - How Much Water?:
If a sprinkler arm is 450 feet long, and the sprinklers are 10 yards
apart, for each gallon of water dumped by the sprinkler 10 yards from the
center, how much water needs to be dumped by the last sprinkler?
- Sept. 16-20 - Circle in a Semicircle: A circle is inscribed in a semicircle. The diameter of the circle and the
radius of the semicircle are 12 units. What is the area of the region of
the semicircle that is outside the circle?
- Sept. 23-27 - Proofs Without Words: Drawings can 'prove' mathematical statements. What picture would prove what (a + b)^2 is equal to? How about
(a + b)(c + d)? - Sept. 30-Oct. 4 - Large Cube and Painted Faces: Unit cubes form a larger cube. Some faces of the larger cube are painted. When the large cube is taken apart, 24 of the unit cubes have no paint on them. How big was the
large cube and which of its faces were painted?
- Oct. 7-11 - Splitting a Hexagon: 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 your pieces? Split a regular hexagon into six identical kites.
- Oct. 14-18 - Polyiamonds: There are twelve different polyiamonds that contain six equilateral triangles each. How can you fit eight of them together to form a six-pointed star?
- Oct. 21-25 - Circle, Hexagon, & Triangle: A regular hexagon and an equilateral triangle share three vertices and are inscribed in a circle with a radius of 8 units. What is the area of the region between the two polygons?
- Oct. 28-Nov. 1 - Six Circle Intersection: What is the maximum number of times six circles of the same size can intersect?
- Nov. 4-8 - Kickoff Return: Herschel Walker received the kickoff on the right hash mark at the 7 yard line and ran it back to the other 7 yard line on the left side of the field for a total of
86 yards. Was the actual distance close to a 100-yard dash?
- Nov. 11-15 - Chords and Arcs: A chord of
a circle is the hypotenuse of an isosceles right triangle whose legs are
radii of the circle. The radius of the circle is 6 times the square root of
2. What is the length of the minor arc subtended by the chord?
- Nov. 18-22 - Dissecting Shapes: 1) Take the irregular shape shown and, making just two cuts, turn it into a square. 2) Take a square and, using four cuts, make five smaller equal squares whose total area is the same as the original.
- Nov. 25-Dec. 6 - Circle, Semicircle, and Squares: Take a circle and two squares. One square has the diameter of the circle as an edge; the other square is inscribed in the circle. What's the area of the small square compared to the big one? What if the small square were inscribed in the semicircle?
- Dec. 9-13 - Overlapping Squares: Two congruent 10cm x 10cm squares overlap. A vertex of one square is at the center of the other square. What is the largest possible value for the area where they overlap? (The one square is movable, as long as the vertex remains in the center.)
- Dec. 16-20 - Circle and Rhombus: In the picture, we have a circle and a rhombus. BC is 6, AE is 4,
<DAE is 45 degrees, and AD is a diameter of the circle. How far is it
around the perimeter of the whole figure?
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