Answer:
The height is 24 centimeters
Explanation:
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