Question

The surface area of the triangular prism pictured below is 204 square centimeters. What is the height of the prism?

Answer 1

The picture in the attached figure

we know that
surface area=2*area of the base+perimeter*height

area of the base=area of the triangle
area of the base=3*4/2----> 6 cm²

perimeter of the base=perimeter of triangle
perimeter=3+4+5----> 12 cm
height=x cm

surface area=2*6+12*x
surface area=204 cm²
12+12*x=204
12*x=204-12
12*x=192
x=192/12
x=16 cm

the answer is
16 cm