"What is the area? You should be able to solve this"

[ijabbott]

(08-06-2018 09:14 PM)Jim Horn Wrote:  Same answer, different approach - I considered the half-side segments (marked with the two short dashes) as of length "h" each and labeled all 9 vertices by their coordinates [0,0], [h,0], [2h,0], etc. Then found the areas of each of the four sections using the Shoelace Formula mentioned earlier here (thanks!). That gave me four equations in four unknowns. A bit of quick algebra gave h is the square root of 24 and the missing area as 28 for an overall area of 96. Fun - and thank you!

That's the way I did it too, although the method shown in the youtube video is simpler!

A similar method to the shoelace method is to split or extend each quadrilateral into a trapazoid/trapezium and a right triangle (which is either added to or subtracted from the trapezoid/trapezium to get the overall area of the quadrilateral). This gives the same four equations as the shoelace formula.