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?
To find the total surface area of the figure, we need to calculate the surface area of each rectangular prism separately and then add them together.
Surface area of the left rectangular prism:
- Top and bottom faces: 10mm x width
- Front and back faces: 8mm x width
- Right and left faces: 10mm x 8mm
Surface area of the right rectangular prism:
- Top and bottom faces: 6mm x 6mm
- Front and back faces: 6mm x 6mm
- Right and left faces: 6mm x 6mm
Now, the total surface area of the figure can be calculated by adding up the surface areas of the two rectangular prisms:
Total surface area = (10mm x width + 8mm x width + 10mm x 8mm) + (6mm x 6mm + 6mm x 6mm + 6mm x 6mm)
Total surface area = (10w + 8w + 80) + (36 + 36 + 36)
Total surface area = 18w + 188
Given that the combined length of the two rectangular prisms is 16mm, we can calculate the total surface area using the total length:
16 = 10 + 6
16 = 18w + 188
18w = -172
w = -9.55
Since the width cannot be negative, there seems to be a mistake in the provided information or calculations. Please double-check the dimensions and calculations before finding the total surface area.