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Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?
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How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?
The Cyclic Quadrilateral
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Age 11 to 14
Challenge Level
You'll have to use some experimentation here, to get a feel for what does and doesn't work.
Do you think you could fill the whole grid using just one shape, if you chose the right 8 cards? What sort of quadrilateral might have lots of nice properties?
It's pretty obvious that you can't come up with a shape that has just 1 axis of symmetry and more than 1 axis of symmetry, so if you put one of these at the start of a row and the other at a start of a column, you know that you won't be able to fill in the square where they intersect. Can you think of any other combinations like this? Is it possible to choose them so that you can't fill in any of the squares?
Do you think you could fill the whole grid using just one shape, if you chose the right 8 cards? What sort of quadrilateral might have lots of nice properties?
It's pretty obvious that you can't come up with a shape that has just 1 axis of symmetry and more than 1 axis of symmetry, so if you put one of these at the start of a row and the other at a start of a column, you know that you won't be able to fill in the square where they intersect. Can you think of any other combinations like this? Is it possible to choose them so that you can't fill in any of the squares?
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.