SOLUTION: What is the surface area of an equilateral triangular prism when the height is 10 and each side is 8? (it's an equilateral triangle )

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Question 27936: What is the surface area of an equilateral triangular prism when the height is 10 and each side is 8? (it's an equilateral triangle )
Answer by bmauger(101) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of any prism is the area of the base times the height. So you need to find the area of an equilateral triangle with sides of 8.
On paper, divide the equilateral triangle in half from one angle of the triangle to the opposite base. This will serve as the height of the triangle. Your half triangles have angles of 30, 60, and 90. And has sides across of 8, 4, and ?.
Using the pythagorean theorem to find the other base.
c%5E2=a%5E2%2Bb%5E2
8%5E2=4%5E2%2Bb%5E2
64=16%2Bb%5E2
48=b%5E2
sqrt%2848%29=b
4sqrt%283%29=b

Area of a triangle=1/2*base*height
A=bh%2F2
A=8%2A4sqrt%283%29%2F2
A=16sqrt%283%29
Volume of prism =Area*height
V=ah
V=16sqrt%283%29%2A10
V=160sqrt%283%29