To find the total surface area of the figure, we first calculate the surface area of the outer rectangular prism and then subtract the surface area of the missing section.
The surface area of the outer rectangular prism can be calculated by finding the area of each face and summing them together:
- Top and bottom faces: 15 inches * 6 inches * 2 = 180 square inches
- Front and back faces: 15 inches * 12 inches * 2 = 360 square inches
- Left and right faces: 6 inches * 12 inches * 2 = 144 square inches
Total surface area of the outer rectangular prism = 180 + 360 + 144 = 684 square inches
Now we calculate the surface area of the missing section:
- Top and bottom faces: 7 inches * 6 inches * 2 = 84 square inches
- Front and back faces: 7 inches * 12 inches * 2 = 168 square inches
- Left and right faces: 6 inches * 12 inches * 2 = 144 square inches
Total surface area of the missing section = 84 + 168 + 144 = 396 square inches
Finally, the total surface area of the figure is the surface area of the outer rectangular prism minus the surface area of the missing section:
Total surface area = 684 - 396 = 288 square inches
Therefore, the total surface area of the figure is 288 square inches.
wer 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)
1 answer