△abc∼△def , △abc has a height of 14 centimeters, and △def has a height of 6 centimeters. what is the ratio of the area of △abc to the area of △def ?

Since triangle ABC is similar to triangle DEF then the ratio of the corresponding sides is constant.
The ratio of the corresponding lengths is referred to as the linear scale factor.
Considering the heights of the two triangles;
L.S.F = 14/6
          = 7/3
The ratio in area (A.S.F) is given by (L.S.F)²
Therefore, A.S.F = (7/3)² = 49/9
Thus te ratio of the area of triangle ABC to DEF is 49:9