Question

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Surface Area of Composite 3D Figures Practice
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Use the image to answer the question.

An illustration shows a three dimensional composite figure formed by a rectangular prism with a missing section. The missing section is also in the shape of a rectangular prism. The top, right, and front faces of the figure are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism has a length of 15 inches, a width of 6 inches, and a height of 12 inches. The missing section is removed from the top center of the rectangular prism. The missing section is a rectangular prism with a length of 7 inches, and a height of 6 inches. The missing section has the same width as the larger rectangular prism. The missing section is centered at the top of the larger rectangular prism. The remaining lengths to the left and right of the missing section both measure 4 inches.

What is the total surface area of the figure?

(1 point)
in.2

Answer 1

672 in.^2

Work: Original prism SA = 2(15·6 + 15·12 + 6·12) = 684. Removing the top-center 7×6×6 prism removes three outer faces (top, front, back) of area 3(7·6)=126 and exposes three new faces (bottom 7·6 and two side faces 6·6 each) of area 42+36+36=114. So total SA = 684 − 126 + 114 = 672 in.^2.