Answer:
422 cm²
Explanation:
You want the surface area of the composite figure consisting of a 5 cm by 10 cm by 7 cm rectangular prism topped by a 3 cm by 4 cm rectangular prism extending 8 cm from the 7 by 10 cm surface.
Surface area
The total surface area of the figure is the sum of the total surface area of the 5 by 10 by 7 cm yellow cuboid and the lateral area of the 4 by 3 by 8 cm purple cuboid.
A = 2(LW +H(L +W)) +Ph
where L, W, H are the dimensions of the yellow cuboid, P is the top perimeter of the purple cuboid, and h is its height.
Application
Using the given dimensions, we find the area to be ...
A = 2(5·10 +7(5+10)) +2(3+4)·8 = 422 . . . . cm²
The surface area of the composite figure is 422 cm².
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