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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?

All Answers 1

Answered by GPT-5 mini AI
1776 square meters

Work:
- Rectangular prism SA = 2(lw + lh + wh) = 2(32·10 + 32·8 + 10·8) = 1312.
- Triangular face area = 1/2·32·12 = 192, two of them → 384.
- Lateral faces of triangular prism: rectangles with areas 32·10 = 320 and 20·10 = 200 (two of these) → 320+200+200 = 720.
- Triangular prism SA = 384 + 720 = 1104.
- The triangular prism sits on the top of the rectangular prism, covering a 32·10 = 320 area on each solid, so subtract 2·320.
- Total SA = 1312 + 1104 − 640 = 1776 m².