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
The total surface area of the figure can be calculated by adding up the surface areas of each face of the two rectangular prisms.
For the smaller rectangular prism on the left:
- The top face has an area of 10mm x 8mm = 80mm^2
- The front face has an area of 10mm x 6mm = 60mm^2
- The side faces have areas of 8mm x 6mm = 48mm^2 each, so a total of 2 x 48mm^2 = 96mm^2
Adding those up, the total surface area for the smaller rectangular prism is 80mm^2 + 60mm^2 + 96mm^2 = 236mm^2
For the larger rectangular prism on the right:
- The top face has an area of 6mm x 6mm = 36mm^2
- The front face has an area of 6mm x 6mm = 36mm^2
- The side faces have areas of 6mm x 6mm = 36mm^2 each, so a total of 2 x 36mm^2 = 72mm^2
Adding those up, the total surface area for the larger rectangular prism is 36mm^2 + 36mm^2 + 72mm^2 = 144mm^2
Therefore, the total surface area of the figure is the sum of the surface areas of the two rectangular prisms, which is 236mm^2 + 144mm^2 = 380mm^2.