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?
incorrect
To find the total surface area of the figure, we need to find the surface area of each rectangular prism and then add them together.
For the rectangular prism on the left:
- The surface area of the top and bottom faces = 10mm * width
- The surface area of the front and back faces = 8mm * width
- The surface area of the left and right faces = 10mm * 8mm = 80 square millimeters
For the rectangular prism on the right:
- The surface area of the top and bottom faces = 6mm * 6mm = 36 square millimeters
- The surface area of the front and back faces = 6mm * 6mm = 36 square millimeters
- The surface area of the left and right faces = 6mm * 6mm = 36 square millimeters
Adding the surface areas of both rectangular prisms:
= (10mm * width + 8mm * width) + 80 + 36 + 36
= 2*(10mm * width + 8mm * width) + 152
Given that the total length of both rectangular prisms is 16mm, we can find the width:
10mm + 6mm = 16mm
Width = 16mm - 10mm = 6mm
Substitute the value of the width back into the formula:
= 2*(10 * 6 + 8 * 6) + 152
= 2*(60 + 48) + 152
= 2*(108) + 152
= 216 + 152
= 368 square millimeters
Therefore, the total surface area of the figure is 368 square millimeters.
I apologize for the mistake in my previous response. Let's calculate the total surface area of the figure correctly.
Rectangular prism on the left:
- Total surface area = 2(l*w + l*h + w*h) = 2(10*8 + 10*w + 8*w) = 2(80 + 18w), where w represents the width.
Rectangular prism on the right:
- Total surface area = 2(l*w + l*h + w*h) = 2(6*6 + 6*6 + 6*6) = 2(36 + 36 + 36) = 216
Given that the combined length of both rectangular prisms is 16mm:
10 + 6 = 16
Width of the left prism (w) = 16 - 6 = 10mm
Now, substitute the width back into the formula for the left prism:
= 2(80 + 18*10) = 2(80 + 180) = 2(260) = 520
Adding the surface areas of both rectangular prisms:
= 520 + 216 = 736
Therefore, the total surface area of the figure is 736 square millimeters.