You can find are of any triangle by HERON'S fromula if all its sides are known.
Here Sides are - 5 cm, 12 cm and 13 cm.
So, s = (a+b+c+)/2 where a,b, and c are sides of triangle
s = (5+12+13)/2 = 30/2 = 15
So, Area = 30
And the smallest height will be on the largest base. So here the largest side is 13 cm.
So by area formula we have
Area = 1/2 *base * height
But area = 30
so, 30 = 1/2 * 13 *height
height = 60/13 = 4.615 cm