To find the surface area of the triangular prism, we first need to determine the surface areas of the triangular base and the three rectangular faces.
Step 1: Calculate the area of the triangular base.
The triangular face is a right triangle with:
- One leg = 3 cm
- Other leg = 4 cm
The area of a triangle is given by the formula:
Step 2: Determine the dimensions of the prism.
The prism has:
- Width (one side of the triangular face) = 5 cm (this is the height of the prism)
- The length of the prism = 11 cm
Step 3: Calculate the areas of the rectangular faces.
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Rectangular face corresponding to the triangular base (area on the left):
- Width = 5 cm (height of the prism),
- Length = hypotenuse of the triangle.
To find the hypotenuse (c) of the triangle:
Area of this rectangular face:
-
For the right rectangular face (shown in the illustration):
- Width = 5 cm,
- Length = length of the prism = 11 cm.
Area:
-
For the other rectangular face (side face):
- Corresponding to the other leg of the triangle.
- Length = 11 cm.
- Width = 4 cm (one leg of the triangular base).
Area:
Step 4: Total surface area of the prism.
Surface area (SA) of the prism includes:
-
2 triangular bases:
-
3 rectangular faces:
Final Calculation:
\[ \text{Total Surface Area} = \text{Total Area}{\triangle} + \text{Total Area}{\text{rect}} = 12 + 154 = 166 \text{ cm}^2 \]
Thus, the surface area of the triangular prism is 166 square centimeters.