use the image to answer the question
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?
(1 point)
m2
Skip to navigation
To find the total surface area of the figure, we need to calculate the surface area of each prism separately and then add them together.
Surface area of rectangular prism:
- Front and back faces: 2 * length * height = 2 * 32m * 8m = 512m^2
- Top and bottom faces: 2 * length * width = 2 * 32m * 10m = 640m^2
- Side faces: 2 * width * height = 2 * 10m * 8m = 160m^2
Total surface area of rectangular prism = 512m^2 + 640m^2 + 160m^2 = 1312m^2
Surface area of triangular prism:
- Base of the triangular face: 1/2 * base * height = 1/2 * 20m * 12m = 120m^2
- Two sides of the triangular face: 20m * height = 20m * 12m = 240m^2
- Multiply this by 2 since there are two triangular faces: 2 * (120m^2 + 240m^2) = 720m^2
Total surface area of triangular prism = 720m^2
Therefore, the total surface area of the composite figure is 1312m^2 (rectangular prism) + 720m^2 (triangular prism) = 2032m^2.