Draw 2 lines, one starting at T and one starting at U both towards and stopping at the center of the square. You have now made the shaded region into 3 right triangles. If QR = 1, then PT and RU both equal ½ (so do the lines you drew from T and U to the center). Solve the area of these triangles with the formula (1/2)bh:
(1/2) (1/2) (1/2) = 1/8
If the area of one triangle is 1/8, then the area of all 3 triangles is 3 times that much, or 3/8.