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How do you define a rectangle? There are lots of possible definitions, such as:
Splitting the tilted square into right-angled triangles and squares and adding the areas of the different parts:
Boxing in the square, working out the area of the box and subtracting the areas of the unwanted right-angled triangles:
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?
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.