SOLUTION: if all the edges of an equilateral triangular based right prism is s units long, what is the volume of the prism in terms of s. what is the surface area of the prism in terms of s.

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Question 957568: if all the edges of an equilateral triangular based right prism is s units long, what is the volume of the prism in terms of s. what is the surface area of the prism in terms of s.

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
s=length of all edges A=Area; V=volume; SA=surface area; a=altitude of triangular base
The altitude of the triangular base of the prism would be given by:
a=%28sqrt%283%29%2F2%29s
The area of an equilateral triangle in terms of s (base=s) is:
A%5Bbase%5D=%281%2F2%29sa
A%5Bbase%5D=%281%2F2%29s%2A%28sqrt%283%29%2F2%29s
A%5Bbase%5D=%28sqrt%283%29%2F4%29s%5E2
So volume of the prism would be given by (height=s):
V=A%5Bbase%5D%2Aheight
V=%28sqrt%283%29%2F4%29s%5E3
The surface area would be:
2%2AA%5Bbase%5D+Area of sides
Each side would have Area=L%2AW=s%2As=s%5E2
The area of all 3 sides=3s%5E2
.
And 2%2AA%5Bbase%5D=2%28sqrt%283%29%2F4%29s%5E2=%28sqrt%283%29%2F2%29s%5E2
.
SA=%28%28sqrt%283%29%2F2%29s%5E2%29%2B3s%5E2
.
SA=%28s%5E2%29%28sqrt%283%29%2F2%2B3%29