Question

Find the surface area of the composite figure.

2 in.
4 in.
9 in.
SA
=
7 in.
2
[?] in.²
4 in.
4 in.
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Answer 1

236 in²

Explanation:

You want the surface area of the figure comprised of two cuboids.

Area

The surface area of the figure will be the sum of the total surface area of the purple cuboid, plus the lateral surface area of the yellow cuboid.

SA = 2(LW +H(L +W)) + Ph

SA = 2(9·4 +2(9 +4)) +(4·4)(7) = 236 . . . . square inches

The surface area of the composite figure is 236 square inches.

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Additional comment

You can consider the face on the right side to be equal in area to the area of the purple cuboid that is covered by the yellow one. So, figuring the total area of the purple cuboid effectively includes the area of the face on the right side.

Then the remaining part of the area of the yellow cuboid is the area of the four 7×4 rectangles that are its lateral area.

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