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
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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.
Surface area of the rectangular prism:
2lw + 2lh + 2wh
= 2(32)(10) + 2(32)(8) + 2(10)(8)
= 640 + 512 + 160
= 1312 square meters
Surface area of the triangular prism:
The base of the triangular prism is the same as the base of the rectangular prism, so we only need to find the area of the two triangular faces.
Area of one triangular face:
1/2 * base * height
= 1/2 * 20 * 12
= 120 square meters
Total surface area of the figure:
1312 + 2(120)
1312 + 240 = 1552 square meters
Therefore, the total surface area of the figure is 1552 square meters.