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 13.7 centimeters and a height of 11.5 centimeters. The missing section is removed from the bottom right corner of the rectangular prism. The missing section is a rectangular prism that shares a width of 3 centimeters with the rest of the figure. The missing rectangular prism section has a length of 7.5 centimeters and a height of 7.5 centimeters. The remaining length to the left of the missing section both measures 6.2 centimeters. The remaining height above the missing section measures 4 centimeters.Solve for the total surface area of the figure.
To find the total surface area of the figure, we first need to find the surface area of the rectangular prism without the missing section and then subtract the surface area of the missing section.
Surface area of the rectangular prism without the missing section:
Top and bottom faces: 2 * (length * width) = 2 * (13.7 * 11.5) = 314.9 cm²
Front and back faces: 2 * (length * height) = 2 * (13.7 * 11.5) = 314.9 cm²
Left and right faces: 2 * (width * height) = 2 * (11.5 * 4) = 92 cm²
Total surface area of the rectangular prism without the missing section = 314.9 + 314.9 + 92 = 721.8 cm²
Surface area of the missing section:
Top and bottom faces of the missing section: 2 * (3 * 7.5) = 45 cm²
Front and back faces of the missing section: 2 * (7.5 * 7.5) = 112.5 cm²
Left and right faces of the missing section: 2 * (3 * 7.5) = 45 cm²
Total surface area of the missing section = 45 + 112.5 + 45 = 202.5 cm²
Therefore, the total surface area of the figure is 721.8 - 202.5 = 519.3 cm².