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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?

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
7 months ago

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.

Surface area of the larger rectangular prism:
- Front and back faces: 6mm x 6mm = 36mm^2 x 2 = 72mm^2
- Top and bottom faces: 6mm x 10mm = 60mm^2 x 2 = 120mm^2
- Left and right faces: 6mm x 10mm = 60mm^2 x 2 = 120mm^2

Total surface area of larger rectangular prism = 72mm^2 + 120mm^2 + 120mm^2 = 312mm^2

Surface area of the smaller rectangular prism:
- Front and back faces: 6mm x 8mm = 48mm^2 x 2 = 96mm^2
- Top and bottom faces: 6mm x 10mm = 60mm^2 x 2 = 120mm^2
- Left and right faces: 6mm x 8mm = 48mm^2 x 2 = 96mm^2

Total surface area of smaller rectangular prism = 96mm^2 + 120mm^2 + 96mm^2 = 312mm^2

Total surface area of the figure = 312mm^2 + 312mm^2 = 624mm^2

Therefore, the total surface area of the figure is 624 square millimeters.