To find the surface area of the net of the triangular prism, we need to calculate the area of both the triangular bases and the rectangular lateral surfaces.
-
Area of the triangular base: The area \( A \) of a triangle is calculated using the formula: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \] Here, the base is 16 meters and the height is 15 meters. Thus, \[ A = \frac{1}{2} \times 16 \times 15 = 120 \text{ square meters} \]
Since there are two triangular bases, the total area for the triangular bases is: \[ A_{\text{triangles}} = 2 \times 120 = 240 \text{ square meters} \]
-
Area of the rectangular lateral surfaces: The prism has three rectangular lateral surfaces. Let's calculate each one:
-
Right rectangular face: This has a base of 16 meters and a height (width of the prism) of 11 meters: \[ A_{\text{rect1}} = 16 \times 11 = 176 \text{ square meters} \]
-
Left rectangular face: This rectangle uses the left side of the triangle (17 meters) as the height and the same width (11 meters): \[ A_{\text{rect2}} = 17 \times 11 = 187 \text{ square meters} \]
-
Back rectangular face: This rectangle uses the right side of the triangle (17 meters) and the width (11 meters): \[ A_{\text{rect3}} = 17 \times 11 = 187 \text{ square meters} \]
Now, we sum the areas of the rectangular lateral surfaces: \[ A_{\text{rectangles}} = 176 + 187 + 187 = 550 \text{ square meters} \]
-
-
Total surface area of the prism: To find the total surface area, we add the area of the triangular bases to the area of the rectangular lateral surfaces: \[ \text{Total Surface Area} = A_{\text{triangles}} + A_{\text{rectangles}} = 240 + 550 = 790 \text{ square meters} \]
Thus, the surface area of the net of the triangular prism is:
790 square meters.