Surface Area of Composite 3D Figures Practice Complete this assessment to review what you've learned. It will not count toward your grade. 1 of 51 of 5 Items Question Use the image to answer the question. What is the total surface area of the figure? (1 point) mm2
1. 353.8 cm^2
2. 408 cm^2
3. 1,171.5 in.^2
4. 330 ft.^2
5. 222 in.^2
Answers for the quick check!! 100% correct
1. 520
2. 1,776
3. 672
4. 380
5. 4,320
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To find the total surface area of the figure, we need to calculate the surface area of each individual shape and then add them together.
The figure consists of a rectangular prism and a triangular prism.
Surface area of rectangular prism:
- The rectangular prism has a length of 8 mm, a width of 4 mm, and a height of 6 mm.
- The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh.
- Plugging in the values, we get:
2(8)(4) + 2(8)(6) + 2(4)(6)
= 64 + 96 + 48
= 208 mm²
Surface area of triangular prism:
- The triangular prism has a base with a width of 4 mm and a height of 6 mm.
- The length of the prism is 8 mm.
- The formula for the surface area of a triangular prism is the area of the two triangular bases plus the lateral surface area.
- Plugging in the values, we get:
2(1/2)(4)(6) + 2(4)(8)
= 24 + 64
= 88 mm²
Total surface area of the figure:
208 mm² (rectangular prism) + 88 mm² (triangular prism) = 296 mm²
Therefore, the total surface area of the figure is 296 mm².