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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?

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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.

# Kite

##### Stage: 3 Challenge Level:

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).