Nets Math Example 3

Solution

1. 1
   Step 1: A triangular prism has 5 faces: 2 triangular faces (bases) and 3 rectangular faces (lateral faces).
2. 2
   Step 2: Area of each triangular base: $\frac{1}{2}(4)(3) = 6$ cm². Both triangular faces: $2 \times 6 = 12$ cm².
3. 3
   Step 3: The three rectangular lateral faces have widths equal to the three sides of the triangle. If the triangle has sides 4, 3, and hypotenuse $\sqrt{16+9} = 5$ cm (right triangle), the lateral areas are $4 \times 10 = 40$, $3 \times 10 = 30$, and $5 \times 10 = 50$ cm².
4. 4
   Step 4: Total SA $= 12 + 40 + 30 + 50 = 132$ cm².