Surface Area of Composite 3D Figures Practice
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Question
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An illustration shows a three dimensional composite figure formed by a smaller rectangular prism connected to a larger rectangular prism. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism on the left has a length of 10 millimeters a height of 8 millimeters. The width of the rectangular prism is not shown, but it aligns perfectly with the width of the rectangular prism on the right. The rectangular prism on the right has a length of 6 millimeters, a width of 6 millimeters, and a height 6 of millimeters. The combined length of the two rectangular prisms measures 16 millimeters.
What is the total surface area of the figure?
(1 point)
mm2
To find the total surface area of the figure, we need to find the surface area of each rectangular prism and then add them together.
For the larger rectangular prism on the right:
Surface area = 2lw + 2lh + 2wh
Surface area = 2(6)(6) + 2(6)(6) + 2(6)(6)
Surface area = 72 + 72 + 72
Surface area = 216 mm2
For the smaller rectangular prism on the left:
Surface area = 2lw + 2lh + 2wh
Surface area = 2(10)(6) + 2(8)(6) + 2(8)(10)
Surface area = 120 + 96 + 160
Surface area = 376 mm2
Therefore, the total surface area of the figure is 216 + 376 = 592 mm2.