What fraction of the square's area is green?

1) Let the side of the square be 2a. Its area will be 4a². 2) The legs of the two large triangles are 2a and a, making their areas = a² (i.e. 2a•a/2), so, both together would be 2a². 3) They overlap in a small triangle which is similar to the large triangles (left to the reader.) 4) The hypotenuse of the small triangle is a. The hypotenuse of the large triangles is a√5, making the ratio of the sides 1/√5... 5) Therefore the legs of the small triangle are a/√5, and 2a/√5. 6) therefore the area of the overlap is (2a²/5)/2, or a²/5. 7) So the colored area is given as: (area of square) - (sum of areas of large triangle - from #2 above) +(area of overlap - from #6 above). Or: 4a² - 2a² + a²/5 => 2a² + a²/5 => 11a²/5 8) Finally, to get the colored area's percentage of area of the square, we divide the area from #7 by the area of the square, or: (11a²/5)/4a² => 11/20 9) Converting 11/20 to a percentage yields: 55% So, that's the answer: 55% Now to watch the video to see if I got it right. -s.west