If you're stuck, try the following applet and click on the checkboxes labeled "Show Hint ##"
Some questions that popped in my mind as I worked on this question:
mrhodotnet, 17 July 2013, Created with GeoGebra
- Is the shaded quadrilateral unique? Is this the only quadrilateral that fits the criteria (given sides and angles)?
- Is it possible to draw another diagram with the same given sides and angles but with different shape?
- Isn't it the case that given only 4 sides of a quadrilateral, there isn't enough information to determine area? If so there may not be enough information to determine area, but if it were the case the question would be pointless.
- Is it possible that the area of the shaded quadrilateral is constant regardless of the shape?
- If the area is constant, let's choose the diagram that is the most calculation friendly and find the area.
- I have the area now. How do I know it's constant? Can I show this? What principles are at work? What can I learn about the special cases (the diagrams that I drew) to show it for the general case?
- Is it possible to show this using trigonometry? How should I break down the quadrilateral? A trapezoid and a triangle? Two triangles? Should I tackle the unshaded area first?
- Let's label the unknown sides and use Pythagorean Theorem to find the relationship between the missing sides. Do the equations simplify?
This is my first time embedding a tweet in a post and embedding a GeoGebra html5 applet instead of a java applet. People really make these things easy to do nowadays. Thanks Twitter and GeoGebra!
Update: Removed tweet embedding until I figure out how to embed without including media.