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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?

### Making Rectangles, Making Squares

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

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.

##### Stage: 3 Challenge Level:

Here is a game you could play with a friend...

Ask your friend to choose one of the shapes, and then try to identify which it is.

Then swap over.
Who can identify the other's shape with the fewest questions?

 Isosceles trapezium Rectangle Rhombus Kite Parallelogram Square Trapezium Arrowhead

You may wish to print out this sheet to record the answers and help you eliminate possible shapes.

Here are some questions you might like to consider:

How many questions do you need to ask to guarantee you know your friend's shape?