Use the image to answer the question.
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
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To find the total surface area of the figure, we need to calculate the surface area of each rectangular prism and then add them together.
For the smaller rectangular prism:
- The surface area of the front and back faces (height x width) is 8 mm x w mm = 8w mm^2
- The surface area of the top and bottom faces (length x width) is 10 mm x w mm = 10w mm^2
- The surface area of the left and right faces (length x height) is 10 mm x 8 mm = 80 mm^2
Total surface area of smaller rectangular prism = 2(8w) + 2(10w) + 2(80) = 16w + 20w + 160 = 36w + 160 mm^2
For the larger rectangular prism:
- The surface area of the front and back faces (height x width) is 6 mm x 6 mm = 36 mm^2
- The surface area of the top and bottom faces (length x width) is 6 mm x 6 mm = 36 mm^2
- The surface area of the left and right faces (length x height) is 6 mm x 6 mm = 36 mm^2
Total surface area of larger rectangular prism = 2(36) + 2(36) + 2(36) = 72 + 72 + 72 = 216 mm^2
Therefore, the total surface area of the figure is the sum of the surface areas of the two rectangular prisms: 36w + 160 + 216 = 36w + 376 mm^2.