What is the surface area of this figure in square centimeters? A.96
B.75
C.84
D.60

9514 1404 393

  A.  96

Step-by-step explanation:

The surface area is the sum of the areas of the two triangular bases and the areas of the three rectangular lateral faces.

  A = 2(1/2)bh + PH

where b is the base of the triangle, h is its height, P is the perimeter of the triangle, and H is the height of the prism.

  A = (3 cm)(4 cm) +(3 +4 +5 cm)(7 cm) = 12 cm² +84 cm²

  A = 96 cm²

The surface area of the triangular prism is 96 square cm.

the answer is c.

step-by-step explanation:

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