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Surface Area of Composite 3D Figures Practice

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An illustration shows a three dimensional composite figure formed by a triangular prism stacked on top of a 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 has a length of 32 meters, a width of 10 meters, and a height of 8 meters. The triangular prism has a rectangular base that is aligned on all edges with the rectangular prism below. The perpendicular height of the triangular prism is marked by a right angle symbol from the top vertex to the center of the triangular face. The height of the triangular face of the prism measures 12 meters. The sides of the triangular faces of the triangular prism measure 20 meters.

What is the total surface area of the figure?

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
7 months ago

To find the total surface area of the composite figure, we need to find the surface area of each individual shape and then add them together.

Surface Area of the rectangular prism:
- Front and back faces: 2(32m x 8m) = 512 square meters
- Top and bottom faces: 2(32m x 10m) = 640 square meters
- Sides: 2(8m x 10m) = 160 square meters

Total surface area of the rectangular prism = 512 + 640 + 160 = 1312 square meters

Surface Area of the triangular prism:
- Base: 32m x 10m = 320 square meters
- Two triangular faces: 2(1/2 x 20m x 12m) = 240 square meters

Total surface area of the triangular prism = 320 + 240 = 560 square meters

Total surface area of the composite figure = 1312 + 560 = 1872 square meters

Therefore, the total surface area of the composite figure is 1872 square meters.