Question

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%

Answer 1

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