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.
Any kite of height a and width b can be
divided along the line of symmetry into two equal triangles.
The area of each triangle is 0.5 x base x height = 0.5 x
b x 0.5 x a = 0.25 x a x b
Since the kite is made up of two such triangles, the area of the
kite is given by:
Area of kite = 0.5 x a x b
This solution was sent in by
Stephen Walker from Aylsham Middle School and was also achieved by
Daniel (Archbishop Sancroft High School), Daniel (West Flegg Middle
School), James(Heacham Middle School).