Question

The figure shown is a triangular prism. How much would it cost to cover the bases and the other three faces with foil that costs $0.22 per square foot?

Answer 1

the complete question in the attached figure

we have to find the surface area first

the area of the base is  A1------- > 5*2=10 ft²

A2 (area of two rectangles faces)---------- > 2*3+2*4=14 ft²

A3 (area of the two triangles faces)

base of triangle------------ > 5---------- > (x)+(x-5)

x²+h²=3²    ------------ > h²=9-x²

(5-x)²+h²=4²----------- > h²=16-(5-x)²

9-x²=16-(5-x)²-------------- >9-x²=16-25-10x-x²----------------- > x=1.8

h²=9-(1.8)²------------ > h=2.4 ft

A3= (5*2.4)*2/2=12 ft²

the surface area total=A1+A2+A3=10+14+12=36 ft²

if $0.22 ------------------------ > 1 ft²

X----------------------------------> 36 ft²

X=36*.22=$7.92

the answer is $7.92