The two triangles are similar. When two figures are similar, the ratios of the lengths of their corresponding sides are equal. We use this fact in order to calculate the height of the bigger triangle. We do as follows:
QP / SL = MN / SL+SR
25 / SL = 35 / SL + 13
SL = 32.5
Area = height x base / 2
Area = SL x MN / 2
Area = 32.5 x 35 / 2 = 568.75