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?
please subtract the connecting sides
To find the total surface area of the figure, we need to find the surface area of each rectangular prism and then subtract the area of the connecting sides.
For the rectangular prism on the left:
- Surface area = 2lw + 2lh + 2wh
- Surface area = 2(10)(8) + 2(10)(6) + 2(8)(6)
- Surface area = 160 + 120 + 96
- Surface area = 376 square millimeters
For the 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 square millimeters
Now, we add the surface areas of the two rectangular prisms:
Total surface area = 376 + 216
Total surface area = 592 square millimeters
However, we must subtract the area of the connecting sides between the two rectangular prisms. The connecting sides are the top and front faces of the larger rectangular prism, which have an area of 6 * 6 = 36 square millimeters each.
Total surface area = 592 - 2(36)
Total surface area = 592 - 72
Total surface area = 520 square millimeters
Therefore, the total surface area of the figure is 520 square millimeters.