geometry
posted by unowen
Please reference the illustration at screenshots<dot>firefox<dot>com/kzZjGCIcg9EMQ0MH/brilliant<dot>org to answer the following question:
What percentage of the square's area is colored blue?
30% 35% 40% 45% 50%

Reiny
Nice question, and I could see your diagram.
Several ways to do this, here is what I thought:
easy to get the equation of BD : y = x + 4
and the equation of AQ = (1/2)x
so for the intersection:
(1/2)x = x + 4
x = 2x + 8
3x=8
x = 8/3
so if we consider AB as the base and 8/3 as the height,
area = (1/2)(4)(8/3) = 16/3
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