If the blue triangle's area is 20, then what is the area of the orange quadrilateral in the given image?

Question

In a square we draw one of the diagonals and one of the vertices is linked to the midpoint of a side.

If the blue triangle's area is 20, then what is the area of the orange quadrilateral?

Answer 1

let the side of the square be x
in similar triangle OAB and ODC AR is half of DC therefore OQ is half of OS=x/3
similarly in triangles APQ and ADC AO being 1/3rd of AC OP=x/3
Hence area of triangle ODA=0.5*x*x/3=20 making x=sqrt(120)=10.9544
Area of triangle AOR=0.5*(x/2)*x/3=x^2/12=10
Hence Area ORBC=x^2/2-10=50 units