What is the surface area of the prism in square inches?

To find the surface area of a prism, the problem can be approached in one of two ways.

1. Through an equation that uses lateral area

2. Through finding the area of each side and taking the sum of all the faces

Using the second method, it's helpful to realize rectangular prisms contain 6 faces. With that, it's helpful to understand that there are 3 pairs of sides. That is, there are two faces with the same dimensions. Therefore, we really only have three sides for which we need to calculate areas:  

Faces 1 & 2:

15⋅8=120

Faces 3 & 4:

6⋅8=48

Faces 5 & 6:

15⋅6=90

Now, we can add up the areas of all six sides:

120+120+48+48+90+90=516

The surface area is 516units2.

Step-by-step explanation:

i believe the correct answer is b.

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