2023 Cayley Problem 23

In the diagram, ABC is a quarter-circle centred at B. Each of square PQRS, square SRTB and square RUVT has side length 10. Points P and S are on AB, points T and V are on BC, and points Q and U are on the quarter-circle. Line segment AC is drawn. Three triangular regions are shaded, as shown. What is the integer closest to the total area of the shaded regions?

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.