## bekah2297 3 years ago A prism has a right triangle as its base with a hypotenuse that measures 15 meters and legs that measure 9 meters and 12 meters. What is the surface area of this prism if the height of the prism is 11 meters?

1. m_charron2

Basically, a triangular prism looks like this |dw:1335213379196:dw| To find the total surface area of this prism, you can decompose it into all of its 5 faces (2 triangles and 3 rectangles). Is this something you think you can do? I'll show you a quicker method one way or the other, but you just need to understand this part first

2. m_charron2

So, I'll assume that you got it at this point. Now, for the quick way : first, calculate the area of the triangles (the bases of prism) : h*b/2 = 12*9/2 = 54 for one triangle, and since you have 2, 54*2 = 108 for both. Let's put that temporarely in the back of our minds whilst we calculate the rest Now that this is done, you're left with the 3 rectangles. They have something special, these 3 rectangles : they all have the same height (11 in this case). So here is the total area for the 3 of them : 9*11 + 12*11 + 15*11 Since 11 is a common factor to the 3 terms, I suggest we factor it from the addition : 11(9 + 12 + 15) = 396 9+12+15, that looks a lot like the perimeter of your triangle, right? So that's how you can calculate the area of any prism : the area of both bases + (perimeter of the base * height of the prism). So in this case : 2*54 + 11*(9+12+15) = 504 m^2

3. bekah2297

thank you.

4. MACH1303

are u in flvs