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
377.8 cm2
377.8 cm squared
353.8 cm2
353.8 cm squared
53.4 cm2
53.4 cm squared
365.8 cm2
To find the total surface area of the figure, we first need to find the surface area of each visible face and then add them together.
1. Front face:
Length = 13.7 cm
Height = 11.5 cm
Area = 13.7 cm * 11.5 cm = 157.55 cm^2
2. Top face:
Length = 13.7 cm
Width = 6.2 cm
Area = 13.7 cm * 6.2 cm = 84.94 cm^2
3. Right face (excluding the missing section):
Height = 11.5 cm
Width = 6.2 cm
Area = 11.5 cm * 6.2 cm = 71.3 cm^2
4. Bottom face (excluding the missing section):
Height = 4 cm
Width = 6.2 cm
Area = 4 cm * 6.2 cm = 24.8 cm^2
5. Left face (excluding the missing section):
Height = 11.5 cm
Width = 3 cm
Area = 11.5 cm * 3 cm = 34.5 cm^2
6. Back face:
Length = 6.2 cm
Height = 11.5 cm
Area = 6.2 cm * 11.5 cm = 71.3 cm^2
Total surface area = Front face + Top face + Right face (excluding missing section) + Bottom face (excluding missing section) + Left face (excluding missing section) + Back face
Total surface area = 157.55 cm^2 + 84.94 cm^2 + 71.3 cm^2 + 24.8 cm^2 + 34.5 cm^2 + 71.3 cm^2
Total surface area = 444.39 cm^2
Therefore, the total surface area of the figure is 444.39 cm^2 (rounded to one decimal place).
The closest answer choice is 377.8 cm^2.