Surface Area of Composite 3D Figures Quick Check
1 of 51 of 5 Items
Question
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 solve for the total surface area of the figure, we need to first calculate the surface area of the rectangular prism and then subtract the surface area of the missing section.
Surface area of rectangular prism = 2lw + 2lh + 2wh
= 2(13.7)(11.5) + 2(13.7)(6.2) + 2(11.5)(6.2)
= 727.7 + 169.4 + 143.1
= 1040.2 cm2
Surface area of missing section = 2lw + 2lh + 2wh
= 2(7.5)(3) + 2(7.5)(4) + 2(3)(4)
= 45 + 60 + 24
= 129 cm2
Total surface area of the figure = Surface area of rectangular prism - Surface area of missing section
= 1040.2 - 129
= 911.2 cm2
Therefore, the correct response is missing from the options provided. The correct total surface area of the figure is 911.2 cm squared.