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?
To find the total surface area of the figure, we need to calculate the surface area of both the larger rectangular prism and the missing section, and then subtract the surface area of the missing section from the larger rectangular prism.
Surface area of the larger rectangular prism:
- Front and back faces: 2 * (length * height) = 2 * (15 * 12) = 360 sq. inches
- Top and bottom faces: 2 * (length * width) = 2 * (15 * 6) = 180 sq. inches
- Left and right faces: 2 * (width * height) = 2 * (6 * 12) = 144 sq. inches
Total surface area of the larger rectangular prism = 360 + 180 + 144 = 684 sq. inches
Surface area of the missing section:
- Front and back faces: 2 * (7 * 6) = 84 sq. inches
- Top and bottom faces: 2 * (7 * 6) = 84 sq. inches
- Left and right faces: 2 * (6 * 6) = 72 sq. inches
Total surface area of the missing section = 84 + 84 + 72 = 240 sq. inches
Total surface area of the figure = Surface area of the larger rectangular prism - Surface area of the missing section
= 684 - 240
= 444 sq. inches
Therefore, the total surface area of the figure is 444 square inches.