Answer:
- see below for the net
- area: 168 cm²
Explanation:
You want the net and total surface area for the triangular prism shown.
Net
The net diagram is attached. It consists of three rectangles with triangles attached to the ends of the widest rectangle. Of course, these parts can be arranged in any order you find convenient, as long as the common edges match the original prism.
Area
The net shows the area can be computed as the sum of a rectangle 9 cm high and 5+6+5 = 16 cm wide, together with two triangles of base 6 cm and height 4 cm.
A = (9 cm)(16 cm) +2(1/2)(6 cm)(4 cm)
= 144 cm² +24 cm²
= 168 cm²
The total surface area of the prism is 168 cm².
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Additional comment
The formulas for the area of a rectangle and triangle are ...
A = LW . . . . . area of a rectangle of length L and width W
A = 1/2bh . . . . area of a triangle of base b and height h