SOLUTION: A triangular prism has base edges 4cm, 6cm, and 7cm long. Its lateral area is 408cm^2. What is the height?

Algebra ->  Surface-area -> SOLUTION: A triangular prism has base edges 4cm, 6cm, and 7cm long. Its lateral area is 408cm^2. What is the height?      Log On


   

Question 1080243: A triangular prism has base edges 4cm, 6cm, and 7cm long. Its lateral area is 408cm^2. What is the height?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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

The height is 24 centimeters