An 8x5 rectangle. If the bottom left corner is considered (0, 0), then two lines are drawn within the rectangle, from (0, 4) to (8, 1) and from (1, 5) to (7, 0). The smaller two regions of the four these lines cut the rectangle into are shaded. What is their combined area?
Posting work is encouraged ๐
You've got it, it's 6.5. I actually posted this problem because I originally found the answer using trig, which seemed a bit too brute-force-y, especially considering the original source for this problem - I wanted to see if others could/would find the simpler solution that I assumed existed. And you did ^_^
I tried it just using the area of a kite, but ended up with sqrt(2)*sqrt(22.25) and got ~6.67 I made a mistake somewhere I guess.
The issue there is it isn't a kite: The two longer sides don't have equal length - they're sqrt(73)/2 and sqrt(61)/2. So it's a decent approximation but not quite exact.
One doesn't really see this if the image is oriented like that. Rotating your phone or your head so that the vertical axis matches the long diagonal of the 'kite' makes this difference more obvious.