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Parallelogram in the Middle

Weekly Problem 27 - 2013
The diagram shows a parallelogram inside a triangle. What is the value of $x$?

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Weekly Problem 29 - 2008

The seven pieces in this 12 cm by 12 cm square make a Tangram set. What is the area of the shaded parallelogram?


Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Four rods, two of length a and two of length b, are linked to form a kite, as shown in the diagram. The linkage is moveable so that the angles change. What is the maximum area of the kite?

Now suppose the four rods are assembled into a linkage which makes a parallelogram. What is the maximum area of this parallelogram?