To find the probabilities, the first step is to find the areas of the squares
First find the area of the larger square
The length is 2x
A = (2x)^2 = 4x^2
Then we need to find the area of the shaded square
That will be a 45 45 90 triangle so we can find the length of the hypotenuse,h. The hypotenuse is sqrt(2) times the length of the side of the triangle
h = x sqrt(2)
The side length for the shaded square is x sqrt(2) so
A = (x sqrt(2))^2 = 2 x^2
P( shaded area) = shaded area/ total area
= 2 x^2 / 4 x^2 = 1/2
