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.
(1 point)
Responses
A. 53.4 cm2
B. 353.8 cm2
C. 377.8 cm2
D. 365.8 cm2
C. 377.8 cm2
To find the total surface area of the figure, you calculate the surface area of all visible faces.
Surface area of rectangular prism:
- Front face: 13.7 cm * 11.5 cm = 157.55 cm2
- Top face: 13.7 cm * 6.2 cm = 84.94 cm2
- Right face: 11.5 cm * 4 cm = 46 cm2
Surface area of missing section (rectangular prism):
- Front face: 7.5 cm * 7.5 cm = 56.25 cm2
- Top face: 7.5 cm * 3 cm = 22.5 cm2
- Right face: 3 cm * 4 cm = 12 cm2
Adding up all the surface areas:
157.55 cm2 (front face of rectangular prism) + 84.94 cm2 (top face of rectangular prism) + 46 cm2 (right face of rectangular prism) + 56.25 cm2 (front face of missing section) + 22.5 cm2 (top face of missing section) + 12 cm2 (right face of missing section) = 377.8 cm2
Therefore, the total surface area of the figure is 377.8 cm2.