Friday Puzzler -- triangle area

Re: Friday Puzzler -- triangle area

Henry Higginbotham

I get 1/3. Without much of a formal math background, I'm not good at explanations, but . . . .

I labeled the SW corner of the square as A, NW as B, NE as C, SE as D, the midpoint of the north line as E, and the intersection as F.

ABE has an area of 1/4 and BCD has an area of 1/2, but they overlap within BEF.

Line AE increases its X value at twice the rate that BD decreases, so F is at y=2/3, giving BEF a height of 1/3 and a half-base of 1/4, and thus an area of 1/12.

1 - 1/4 - 1/2 + 1/12 = 1/3

Correct!

Alex Y

I really like your solution since it directly calculates the area.

My approach was similar but less direct. I called the area of the pink triangle x, and using the fact that the pink triangle and BEF are similar, with the base of BEF being 1/2 of the pink base, I got 1/2+1/4-x/4+x=1.

True confession: I initially, carelessly, used x/2 as the area of BEF. The result of x=1/2 didn't pass the small test, though. :-)

Even simpler

Henry Higginbotham

Once you notice from the slopes of the two lines that F is at y=2/3, you're there. The base is 1 and the height is 2/3. Why'd I have to slog through the other three triangles to get there?

But that's too easy!

Alex Y

Giving myself a dope slap.