Answer:
334 in²
Step-by-step explanation:
The total surface area of the composite figure is the sum of the total area of the bottom cuboid and the lateral area of the top cuboid.
<h3>Total cuboid area</h3>
The area of a cuboid is given by the formula ...
A = 2(LW +H(L+W))
For the bottom cuboid, the area is ...
A = 2((9 in)(7 in) +(5 in)(9 in +7 in)) = 2(63 in² +5(16) in²) = 286 in²
<h3>Lateral area</h3>
The lateral area of a cuboid is the product of its perimeter and height. The perimeter is the sum of side lengths, or twice the sum of length and width.
LA = Ph = (2(l +w))h
LA = 2(5 in +3 in)(3 in) = 48 in²
<h3>Total composite area</h3>
The total surface area is the sum of the lateral area of the top cuboid and the total area of the bottom cuboid:
SA = (48 in²) +(286 in²) = 334 in²
The surface area of the composite figure is 334 square inches.
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<em>Additional comment</em>
The exposed area of the bottom cuboid is its total area less the area of the very top face.
The exposed area of the top cuboid is its lateral area plus the area of the very top face.
When we add these two exposed areas together, we find the area of the very top face is both subtracted and added from the sum of the total bottom area and the lateral top area. We skipped that step of adding and subtracting, because its net effect is zero.
