Every line segment is an altitude, namely
BD, AB, BC for triangle ABC (angle B is a right-angle)
BD, AD are altitudes for triangle ABD
BD, DC are altitudes for triangle BDC
So in all, altitudes are
BD,AB, BC,AD,DC.
Using metric relations,
BD^2=AD*DC=5*7=35
=>
BD=sqrt(35)=5.916 (to 3 decimal places)
Hence the area of triangle ABC
Area=Base*Height/2 = (5+7)*sqrt(35)/2= 35.496 (to 3 decimal places)
