Geometry Area of sections of a parallelogram

[Wildcat]

1. The area of a parallelogram is 60 square units. A segment is drawn from one vertex to the midpoint of an opposite side. The diagonal is drawn between the other two other vertices. Find the area of the four regions formed.

Homework Equations

3. I found that two of the triangles formed are similar so the ratio of those triangles would be 1/4. The diagonal separates one region into two triangles which would total 30 units and the lower portion made up of a quadrilateral and a triangle would total 30 units. I'm stuck. I can't find another relationship. Help!

OK I constructed the diagram on geometer sketchpad and found the areas, but I'm wondering how it can be done without geometer sketchpad?? region I = 5 region II=10 region III = 20 and region IV (quadrilateral) = 25. Any ideas??

 

[tiny-tim]

Hi Wildcat!

Hint: split region IV into triangles V and VI, and find relations between I II III and V

 

[Wildcat]

Hi Wildcat!

Hint: split region IV into triangles V and VI, and find relations between I II III and V

I did that. And I know from what I did on GSP that One of the triangles say V is congruent to II, but I can't figure out why. Can you give me another hint :)

 

[tiny-tim]

forget congruence, think areas

 

[Wildcat]

forget congruence, think areas

Thanks, I finally got it :)