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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.

Age 11 to 14Challenge Level

Each line is one side of the named quadrilateral. Can you draw the other three sides in the 4 by 4 dotty grids?

If there is more than one possibility, try to find the quadrilateral with the largest area (given in brackets).

An * indicates that there is a “special” quadrilateral with a larger area than the one
given in the brackets. For example, the largest parallelogram might be a square or a rectangle. Take a look at the Getting Started page if you want to find out more about special cases.

 1.  Rectangle (6) 2.  Square (8) 3.  Rectangle (4) 4.  Isosceles        Trapezium (12) 5.  Parallelogram (9*) 6.  Kite (8) 7.  Parallelogram (6) 8.  Square (5) 9.  Kite (12) 10.  Rhombus (4*) 11.  Parallelogram (3*) 12.  Kite (6) 13.  Arrowhead (6)         (Concave Kite) 14.  Kite (8) 15.  Rhombus (8) 16.  Rhombus (3) 17. Arrowhead (4)       (Concave Kite) 18.  Trapezium (9) 19.  Parallelogram (8) 20.  Isosceles         Trapezium (8) 21.  Kite (3) 22.  Arrowhead (4)         (Concave Kite) 23.  Kite (9) 24.  Trapezium (9)

You may find it useful to print this worksheet of the problem.

With thanks to Don Steward, whose ideas formed the basis of this problem.