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.
Surface area of the rectangular prism on the left:
- Front and back faces: 10mm * 8mm + 10mm * 8mm = 160mm²
- Top and bottom faces: 8mm * w (where w is the width, not given)
- Left and right faces: 10mm * w
- Total surface area of the rectangular prism on the left: 160mm² + 8w + 10w
Surface area of the rectangular prism on the right:
- Front and back faces: 6mm * 6mm + 6mm * 6mm = 72mm²
- Top and bottom faces: 6mm * 6mm + 6mm * 6mm = 72mm²
- Left and right faces: 6mm * 6mm + 6mm * 6mm = 72mm²
- Total surface area of the rectangular prism on the right: 72mm² + 72mm² + 72mm² = 216mm²
Total surface area = 160mm² + 8w + 10w + 216mm²
Total surface area = 376mm² + 18w
As the width of the rectangular prism on the left is not given, we cannot calculate the exact total surface area without that information.
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 answer
1 answer