Answer:
4 in
Explanation:
area right : Ar = 5x
area left : Al = 11x
area top : At = 5x
area bottom : Ab = 13x
area front : Afr = rectangle 13×11 minus area triangle
triangle (right-angled) : (11-5)×(13-5)/2 = 24 in²
Afr = 13×11 - 24 = 119 in²
area back = area front = 119 in²
sloped area : As = 10x
all individual shapes in the surface of the object are rectangles except the 2 areas in the front and in the back, where we had to calculate the complete rectangle and then subtract the cut off triangle area.
so, in total we have
414 = 5x+11x+5x+13x+119+119+10x = 44x + 238
176 = 44x
x = 4 in