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
To find the total surface area of the figure, we need to find the surface area of the larger rectangular prism and subtract the surface area of the missing section.
Surface area of larger rectangular prism:
Front and back faces: 2 * (15 inches * 12 inches) = 360 square inches
Top and bottom faces: 2 * (15 inches * 6 inches) = 180 square inches
Left and right faces: 2 * (12 inches * 6 inches) = 144 square inches
Total surface area of larger rectangular prism = 360 + 180 + 144 = 684 square inches
Surface area of missing section:
Top and bottom faces: 2 * (7 inches * 6 inches) = 84 square inches
Front and back faces: 2 * (7 inches * 12 inches) = 168 square inches
Left and right faces: 2 * (6 inches * 6 inches) = 72 square inches
Total surface area of missing section = 84 + 168 + 72 = 324 square inches
Total surface area of the figure = Surface area of larger prism - Surface area of missing section
= 684 square inches - 324 square inches
= 360 square inches
Therefore, the total surface area of the figure is 360 square inches.