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:
- Front and back faces: 10mm (length) * 8mm (height) = 80mm^2
- Top and bottom faces: 10mm (length) * w (width) = 10w mm^2 (where w is the width)
- Left and right faces: 8mm (height) * w (width) = 8w mm^2
For the rectangular prism on the right:
- Front and back faces: 6mm (length) * 6mm (width) = 36mm^2
- Top and bottom faces: 6mm (length) * 6mm (width) = 36mm^2
- Left and right faces: 6mm (width) * 6mm (height) = 36mm^2
Adding all the surface areas together:
80mm^2 + 10w mm^2 + 8w mm^2 + 36mm^2 + 36mm^2 + 36mm^2
Since the total length of both prisms is 16mm, we know that the width of the left prism is 16mm - 6mm = 10mm.
Replace w with 10mm:
80mm^2 + 10(10) mm^2 + 8(10) mm^2 + 36mm^2 + 36mm^2 + 36mm^2
80mm^2 + 100mm^2 + 80mm^2 + 36mm^2 + 36mm^2 + 36mm^2
Now we have:
288mm^2
So, the total surface area of the figure is 288mm^2.
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)
mm2
1 answer