How do I find area of shaded area given side length relationship

Question

Hi I was trying to do this problem but was unable to figure out how to find the shaded region

I tried to use proportionality with the shaded region but I still kept on getting the wrong answer

any hint/tips?

thanks!

Answer 1

Hint...how many of the smaller triangles can you fit in the other spaces?

Answer 2

If the area of the small triangle $\Delta BDE$ is $a$, then the area of $\Delta BFG$ is $4a$, and the area of $\Delta BAC$ is $9a$.

$$20 = 9a - 4a = 5a$$ $$20/5 = a$$ $$a = 4$$

So the small triangle's area is $4$, and the shaded region's area is

$$4a - a = 3a = 3\times 4 = 12$$