Math Problem Solver

Quadrilateral $ABCD$ is a square with $BC = 12$ cm. Semicircles are constructed inside the square on sides $DC$ and $BC,$ as shown. What is the area of the shaded region?

[asy]

pair A, B, C, D, O;

O=(0,0);

A=(-1, -1);

B=(1, -1);

C=(1, 1);

D=(-1, 1);

fill(arc((0, 1), O, C)--arc((1, 0), C, O)--cycle, red+white+white);

draw(arc((0, 1), D, C));

draw(arc((1, 0), C, B));

draw(A--B--C--D--A);

label("$A$", A, W);

label("$B$", B, E);

label("$C$", C, E);

label("$D$", D, W);

label("$O$", O, SW);

label("$12$", (1, 0), E);

[/asy]