Each edge of a right triangular prism is 8 inches in length. What is the surface area of the right triangular prism?
1 answer:
Check the picture below.
since each edge is 8 inches, that simply means the right-triangle has a base of 8 and a height/altitude of 8 as well.
and since the triangular prism is really just two triangles and 3 rectangles, as you see there, we can simply get the area of each figure and sum them up, and that's the surface area of the prism.
![\bf \stackrel{\textit{area of the two triangles}}{2\left[ \cfrac{1}{2}(\stackrel{base}{8})(\stackrel{height}{8}) \right]}~+~\stackrel{\textit{area of the 3 rectangles}}{3(8\cdot 8)}\implies 64+192\implies 256](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Barea%20of%20the%20two%20triangles%7D%7D%7B2%5Cleft%5B%20%5Ccfrac%7B1%7D%7B2%7D%28%5Cstackrel%7Bbase%7D%7B8%7D%29%28%5Cstackrel%7Bheight%7D%7B8%7D%29%20%5Cright%5D%7D~%2B~%5Cstackrel%7B%5Ctextit%7Barea%20of%20the%203%20rectangles%7D%7D%7B3%288%5Ccdot%208%29%7D%5Cimplies%2064%2B192%5Cimplies%20256)
since each edge is 8 inches, that simply means the right-triangle has a base of 8 and a height/altitude of 8 as well.
and since the triangular prism is really just two triangles and 3 rectangles, as you see there, we can simply get the area of each figure and sum them up, and that's the surface area of the prism.
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