Find the surface area of the triangular prism shown below.
units
2
2
squared

544

Step-by-step explanation:

Add up the areas of each face.

A = 2 × ½(12)(8) + 2 × (10)(14) + (12)(14)

A = 96 + 280 + 168

A = 544

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

c.

step-by-step explanation: