A prism has a right triangle as its base with a hypotenuse that measures 5 meters and legs that measure 3 meters and 4 meters. What is the surface area of this prism if the height of the prism is 6 meters?

When I tried to do the problem, I got 102 squared and got it wrong. How do I figure it out correctly?

Question

A prism has a right triangle as its base with a hypotenuse that measures 5 meters and legs that measure 3 meters and 4 meters. What is the surface area of this prism if the height of the prism is 6 meters? 

When I tried to do the problem, I got 102 squared and got it wrong. How do I figure it out correctly?

anonymous · Answer

surface area is the sum of the individual sides's areas

anonymous · Answer

so you start with the base

anonymous · Answer

4*3/2 = 6

anonymous · Answer

now do the vertical sides above the two legs

anonymous · Answer

4 * 6/2 = 12
3 * 6/2 = 9

anonymous · Answer

now do the face above the hypotenuse

anonymous · Answer

there are a few ways of doing this

anonymous · Answer

the easiest would probably be with trigonometric functions. Have you covered those yet?

anonymous · Answer

Yes. You mean sin and cosine, right?

anonymous · Answer

yes

anonymous · Answer

so we know the base is 5, the harder part is finding the height.

anonymous · Answer

actually, now that I think about it this method does not require trig anyway.

anonymous · Answer

but whatever

anonymous · Answer

xD
Okay

anonymous · Answer

The problem also says "What is the surface area of this prism if the height of the prism is 6 meters? " if that is height we are trying to find.

anonymous · Answer

not quite

anonymous · Answer

we need to find the height of the face, not of the prism

anonymous · Answer

Oh, okay.

anonymous · Answer

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