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?
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.
For the rectangular prism on the left:
Surface Area = 2lw + 2lh + 2wh
Surface Area = 2(10)(w) + 2(10)(8) + 2(8)(w)
Surface Area = 20w + 160 + 16w
Surface Area = 36w + 160
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
Total surface area of the figure:
Total Surface Area = Surface Area of Left Prism + Surface Area of Right Prism
Total Surface Area = 36w + 160 + 72
Total Surface Area = 36w + 232
Since the total length of the figure is 16 millimeters, we can find the width (w) by subtracting the sum of the two lengths of the rectangular prisms from the total length:
16 = 10 + 6 + 2w
16 = 16 + 2w
2w = 0
w = 0
Therefore, the total surface area of the figure is 232 square millimeters.