Question

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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?

(1 point)
m2

Answer 1

1776 m^2

Work:
- Rectangular prism SA = 2(32·10 + 32·8 + 10·8) = 1312. Top (32·10 = 320) is covered, so rect ext = 1312 − 320 = 992.
- Triangular prism: triangle area = 1/2·32·12 = 192, so 2 triangles = 384. Lateral area = perimeter(32+20+20)=72 times depth 10 = 720. Full tri. prism SA = 384+720 = 1104. The bottom rectangle (32·10 = 320) is internal, so tri. ext = 1104 − 320 = 784.
- Total = 992 + 784 = 1776 m^2.