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Linkage

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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Making Rectangles, Making Squares

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

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The Cyclic Quadrilateral

This gives a short summary of the properties and theorems of cyclic quadrilaterals and links to some practical examples to be found elsewhere on the site.

An Equilateral Triangular Problem

Age 11 to 14 Challenge Level:
What angles/areas do you know?
How can you use the angles/areas you know to work out other angles/areas?
What properties does a trapezium/parallelogram/rectangle have?