To calculate the total surface area of the triangular prism represented by the net in the illustration, we need to find the areas of each part of the net: the two triangular bases and the three rectangular sides.
Step 1: Calculate the area of the triangular bases
The area \( A \) of a triangle is given by the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
For the triangular bases:
- The base of the triangle is 9 cm.
- The height is 7.8 cm.
Calculating the area of one triangular base:
\[ A_{triangle} = \frac{1}{2} \times 9 \times 7.8 = \frac{1}{2} \times 70.2 = 35.1 , \text{cm}^2 \]
Since there are two triangular bases, the total area for both is:
\[ A_{triangles} = 2 \times 35.1 = 70.2 , \text{cm}^2 \]
Step 2: Calculate the area of the rectangular sides
There are three rectangular sides:
- Two rectangles corresponding to the legs of the triangle:
- Each rectangle has a length of 17 cm (the length of the prism) and a width of 9 cm (the height of the triangle).
So the area of each of these two rectangles is:
\[ A_{rectangle} = \text{length} \times \text{width} = 17 \times 9 = 153 , \text{cm}^2 \]
Thus, the total area for the two rectangles is:
\[ A_{rectangles (sides)} = 2 \times 153 = 306 , \text{cm}^2 \]
- The third rectangle (the bottom) also has dimensions of 17 cm by 9 cm:
\[ A_{rectangle (bottom)} = 17 \times 9 = 153 , \text{cm}^2 \]
Step 3: Calculate the total surface area
Now we combine all the areas we have calculated:
\[ \text{Total Surface Area} = A_{triangles} + A_{rectangles (sides)} + A_{rectangle (bottom)} \]
\[ \text{Total Surface Area} = 70.2 + 306 + 153 \]
\[ \text{Total Surface Area} = 529.2 , \text{cm}^2 \]
Thus, the total surface area of the triangular prism represented by the net is:
\[ \boxed{529.20} , \text{cm}^2 \]