Two equilateral triangles are glued, and their opposite vertices are connected. If the larger equilateral triangle has an area of 225 and the smaller equilateral triangle has an area of 100, what is the area of the shaded region?
[asy]
size(4cm);
draw((0,0)--(3,0)--(3/2,3sqrt(3)/2)--(0,0));
draw((0,0)--(2,0)--(1,-sqrt(3))--(0,0));
draw((1,-sqrt(3))--(3/2,3sqrt(3)/2));
filldraw((0,0)--(6/5,0)--(3/2,3sqrt(3)/2)--cycle, gray);
[/asy]<spanclass=′latex−bold′>(A)</span>60<spanclass=′latex−bold′>(B)</span>90<spanclass=′latex−bold′>(C)</span>96<spanclass=′latex−bold′>(D)</span>108<spanclass=′latex−bold′>(E)</span>120