To find the total surface area of the figure, first find the surface area of the rectangular prism by adding up the areas of each face (front, back, top, bottom, left, right).
The area of the front face is 13.7 cm * 11.5 cm = 157.55 cm^2
The area of the back face is also 157.55 cm^2
The area of the top face is 13.7 cm * 6.2 cm = 84.94 cm^2
The area of the bottom face (after removing the missing section) is (13.7 cm - 3 cm) * 6.2 cm = 76.54 cm^2
The area of the left face is 11.5 cm * 4 cm = 46 cm^2
The area of the right face is also 46 cm^2
Total surface area of the rectangular prism = 157.55 + 157.55 + 84.94 + 76.54 + 46 + 46 = 568.58 cm^2
Now, find the surface area of the missing section which is a rectangular prism:
The front face of the missing section is 3 cm * 7.5 cm = 22.5 cm^2
The top face of the missing section is 7.5 cm * 4 cm = 30 cm^2
The right face of the missing section is 3 cm * 4 cm = 12 cm^2
Total surface area of the missing section = 22.5 + 22.5 + 30 + 30 + 12 + 12 = 129 cm^2
Finally, subtract the surface area of the missing section from the total surface area of the rectangular prism:
568.58 cm^2 - 129 cm^2 = 439.58 cm^2
Therefore, the total surface area of the figure is 439.58 cm^2.
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
53.4 cm2
53.4 cm squared
353.8 cm2
353.8 cm squared
377.8 cm2
377.8 cm squared
365.8 cm2
1 answer