The area of a triangle is 1/2 the base (b) length times the height (h), where b is one of the three sides and h is the perpendicular line segment drawn from point opposite from the base to the base. If we choose the 12 mm side as b, then h will divide b into 2 shorter segments, x and 12-x. Since the height segment intersects perpendicularly, that divides the original triangle into 2 smaller right triangles, one with sides 9, h and x and the other with sides 6, h and 12-x. By the Pythagoras theorem (a2+b2=c2) this means
91=h2+x2 and 36=h2+(12-x)2
By modifying one of the equations to give h2 in terms of x and then substituting into the other equation, you can derive the value of x. Once you know x, you can determine h and then plug that and 6 (1/2 b) into the equation to determine the area.