What is the total surface area for a rectangular prism with dimensions of 7 cm 2cm 8cm in square centimeters

172 cm^2

Step-by-step explanation:

Since it is a rectangular prism, you would have 6 sides, with two of them being the same. Each side is the values but multiplied by each other. So 7x2, 8x2, and 7x8. If you add them up it would be 14+16+56= 86, but that is only 3 sides, so you need to multiply 86 by 2, thus 172.

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we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4