Answer to Question #6279 in Geometry for Elizabeth Mobley

Consider triangle ABC:

We know that AB=BC=7 cm, AC=5cm.
Let's draw height BD. As long as AC=BC , the height BD is also a median: AD=DC=AC/2=2.5
Consider triangle BDC, its right angled. Let's find BD using Pethagorean theorem:
BD^2+DC^2=BC^2
Hence BD=sqrt(BC^2-DC^2)=sqrt(7^2-2.5^2)= approx. 6.54
Now we can find area:
S=1/2*AC*BD=1/2*5*6.54=16,35 cm²