ABC and DEF are similar isoceles triangles. AB=BC=5cm, AC=6cm, DF=12cm. What is the area of DEF?

We first split ABC into two right-angled triangles. We name the midpoint of AC, M. AM=1cm, and BM=sqrt(5²-3²)=4 by Pythagoras. The area of ABC =1/2ACBM=1/264=12. We can see that the side lengths of DEF are greater than the side lengths of ABC by a factor of two. The area is therefore greater than ABC by a factor of 2²=4. So the area of DEF=4*12=48