I ran into this exercise a couple of days ago and originally thought it had no business in the collegiate level textbook where I found it because it was so simple. (notice that two of the vertices are not on a known point).
The exercise asks:
a) find the area of the quadrilateral
b) prove your solution
Given: The vertical and horizontal distance between any two dots (pegs in geoboard speak) is 1 unit. (As you probably suspected).
[IMG]file:///C:/Users/Terry/AppData/Local/Temp/moz-screenshot-48.png[/IMG] I was able to find the area using trig and a fair bit of algebra. However, I haven't been able to find an applicable Euclidean theorem to do the trick. My instincts tell me to apply the mid-segment theorem, but that idea hasn't done much to solve the exercise.
Thanks for reading!