Step-by-step Answer:
We know the base of triangle ABC = 5, and the area = 15, so by the area formula, the height h can be solved:
area = (1/2) base * height
15=(1/2)(5)h
h=6 = BE
We are given BD=4, DE=3, and BE=h=6
Area, by Heron's formula can be found:
s=(1/2)perimeter=(1/2)(6+4+3)=6.5
Area = sqrt(6.5*(6.5-6)*(6.5-4)*(6.5-3))=5.333
Round to the tenth to get 5.3 square units.