two circles of radii 2cm and 4cm touch each other.find the are of triangle formed by drawing all the three tangents of the circle?

Please draw the diagram to understand the question better. Draw 2 circles which touch each other. Let the center of smaller circle be O and that of bigger circle be O'. Now draw the common tangents and to form the triangle. Let this bigger triangle be ABC. Let it touches the smaller circle at D and E and let it touches the bigger circle at F and G. Draw a line from A which passes through the centers of both the circles and intersects BC at M. Draw a line which passes through the point where two circles touch each other. Let these points be p and q. Let the point where circles touch each other be t
PD = PT = y (say)
PT = PF, so PF = y
Similarly,
TQ = EQ =GQ =y.
Triangle ADO is similar to triangle AFO's
So x/2 = x+2y/4 => x = 2y
So the perimeter of the triangle is 2x+4y => 8y
Now smaller circle is the incenter for the required triangle.
So A/S =inradius
Applying hero's formula for area we get
rt(4y*y*y*2y)/4y = 2
=> y =2rt2 .
Putting this value of y in area formula, we get
rt(8*64) = 16rt2.
So the required are is 16rt2