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)
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 rectangular prism on the left:
Surface area = 2lw + 2lh + 2wh
= 2(10)(8) + 2(10)(w) + 2(8)(w)
= 160 + 20w + 16w
= 160 + 36w
For the rectangular prism on the right:
Surface area = 2lw + 2lh + 2wh
= 2(6)(6) + 2(6)(6) + 2(6)(6)
= 72 + 72 + 72
= 216
Total surface area = Surface area of left prism + Surface area of right prism
= 160 + 36w + 216
= 376 + 36w
Therefore, the total surface area of the figure is 376 + 36w square millimeters.