Answer:
136 square units
Step-by-step explanation:
A "net" is a map of the surfaces of the prism. If you cut it out and fold along the solid lines, you can shape it into the triangular prism it represents. The area of the net is the area of the prism.
As with any composite figure, its area can be found by decomposing it into parts whose area formulas you know. Here, the net can be cut along the horizontal lines to form a rectangle and two triangles.
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rectangle
The rectangle has an overall length of 5+6+5 = 16 units, and a width of 7 units. Its area is ...
A = LW
A = (16)(7) = 112 . . . . square units
triangles
Each triangle has a base of 6 units and a height of 4 units. Its area is ...
A = 1/2bh
A = 1/2(6)(4) = 12 . . . . square units
total area
The composite figure shown has been decomposed into one rectangle and two triangles, so its total area is ...
rectangle area + 2 × triangle area
= 112 + 2×12 = 136 . . . . square units
The surface area of the triangular prism is 136 square units.
