Question 1080243
The perimeter of the triangle base is P = a+b+c = 4+6+7 = 17 cm long.


The lateral surface area (abbreviated LSA) of any prism can be found using this formula


LSA = P*h


where P is the perimeter along the base and h is the height of the prism. 
We're given the lateral area of 408, so LSA = 408. 
Let's use that LSA value, along with P = 17 as well to solve for h.


LSA = P*h
408 = 17*h
408/17 = 17*h/17
24 = h
h = 24


<font color=red>The height is 24 centimeters</font>