By decomposing the design into two rectangular prisms, the surface area of the design is calculated as: A. 256 in.²
What is the Surface Area of a Rectangular Prism?
The surface area of a rectangular prism is expressed as, S = 2(lw + lh + wh).
The design can be decomposed into top rectangular prism and bottom rectangular prism.
The surface area of the design = surface area of the top rectangular prism + surface area of the bottom rectangular prism - 2(area of the top rectangular prism that joins the bottom rectangular prism)
Surface area of the top rectangular prism = 2(lw + lh + wh) = 2(5×4 + 5×4 + 4×4) = 112 in.²
Surface area of the bottom rectangular prism = 2(lw + lh + wh) = 2(8×5 + 8×4 + 5×4) = 184 in.²
Area of the top rectangular prism that joins the bottom rectangular prism = l × w = 5 × 4 = 20 in.²
The surface area of the design = 112 + 184 - 2(20) = 256 in.²
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