Task 1342

The task

Sandy's daughter has a playhouse in the back yard. She plans to cover the one shaded exterior wall and the two rectangular faces of the roof, also shaded, with a special siding to resist the elements. The siding is sold only in 8-foot by 12-foot sections that cost $\$27.30$ each. If Sandy can cut the siding when she gets home, how many dollars will be the cost of the siding Sandy must purchase? [asy] import three; size(101); currentprojection=orthographic(1/3,-1,1/2); real w = 1.5; real theta = pi/4; string dottedline = "2 4"; draw(surface((0,0,0)--(8,0,0)--(8,0,6)--(0,0,6)--cycle),gray(.7)+opacity(.5)); draw(surface((0,0,6)--(0,5cos(theta),6+5sin(theta))--(8,5cos(theta),6+5sin(theta))--(8,0,6)--cycle),gray(.7)+opacity(.5)); draw(surface((0,5cos(theta),6+5sin(theta))--(8,5cos(theta),6+5sin(theta))--(8,10cos(theta),6)--(0,10cos(theta),6)--cycle),gray (.7)+opacity(.5)); draw((0,0,0)--(8,0,0)--(8,0,6)--(0,0,6)--cycle,black+linewidth(w)); draw((0,0,6)--(0,5cos(theta),6+5sin(theta))--(8,5cos(theta),6+5sin(theta))--(8,0,6)--cycle,black+linewidth(w)); draw((8,0,0)--(8,10cos(theta),0)--(8,10cos(theta),6)--(8,5cos(theta),6+5sin(theta)),linewidth(w)); draw((0,0,0)--(0,10cos(theta),0)--(0,10cos(theta),6)--(0,0,6),linetype(dottedline)); draw((0,5cos(theta),6+5sin(theta))--(0,10cos(theta),6)--(8,10cos(theta),6)--(8,0,6),linetype(dottedline)); draw((0,10cos(theta),0)--(8,10cos(theta),0),linetype(dottedline)); label("8' ",(4,5cos(theta),6+5sin(theta)),N); label("5' ",(0,5cos(theta)/2,6+5sin(theta)/2),NW); label("6' ",(0,0,3),W); label("8' ",(4,0,0),S); [/asy]