The right prism shown has a surface area of 414 in.² what is the value of X in inches

4 in

Step-by-step 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

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)