It is given that the area of square ABCD is 6 + 3 sqrt(3). Find the area of square MNPQ.
I'll give you some very worthwhile direction.
1) Think of this as a coordinate geometry prob where A is at the origin, B is on the x axis and D is on the y axis.
2) What is the side length of the big square?
3) What is the equation of QN? What is the half length of AB
4) Arc DQPB is a quarter of a circle. What is the equation of that circle?
5) Find Q (intersection of a circle and a line)
6) What is the coordinates of the centre of the two squares? Call it X
7) What is the distance QX?
8) What is the diagonal lengths of the little square?
9) Now you have all the info you need to work out the area of the little square.
If you have questions you can ask but I will want you to show me that you have put some of your own effort in.
Please no one do this for guest. This is a teaching answer.