The formula for determining the area of a traingle is expressed as
Area = 1/2 * base * height
For triangle ABC,
height = 6
area = 30
Thus,
30 = 1/2 * base * 6
30 = 3 * base
base = 30/3 = 10
If two triangles are similar, it means that the ratio of their corresponding sides is equal. Thus,
Height of traingle ABC/ Height of traingle DEF = Base of traingle ABC/ base of traingle DEF
Thus, we have
6/Height of traingle DEF = 10/15
6/Height of traingle DEF = 2/3
By cross multiplying, we have
2 * Height of triangle DEF = 3 * 6 = 18
Height of triangle DEF = 18/2 = 9
Thus, area of triangle DEF is
Area = 1/2 * 15 * 9 = 67.5
The correct option is C