To calculate the surface area of a triangular prism, you need to find the areas of all the faces and then sum them up. A triangular prism has two triangular bases and three rectangular faces.
The given dimensions are somewhat limited, so I'll assume the following based on common interpretations:
- The triangular base has a base length (b) of 5 cm and a height (h) of 3 cm.
- The prism has a length (l) of 11 cm.
- One side of the triangle is 4 cm (which suggests the side length of the triangular base).
Now, let's break it down step by step:
1. **Area of one triangular base**:
\( A_{\text{triangle}} = \frac{1}{2} \times b \times h = \frac{1}{2} \times 5 \times 3 = \frac{15}{2} = 7.5 \, \text{cm}^2 \)
Since there are two triangular bases:
\( \text{Total area of triangular bases} = 2 \times 7.5 = 15 \, \text{cm}^2 \)
2. **Areas of the three rectangular faces**:
- One rectangle with dimensions 5 cm (base of the triangle) and 11 cm (length of the prism):
\( A_{\text{rectangle1}} = 5 \times 11 = 55 \, \text{cm}^2 \)
- Another rectangle with dimensions 3 cm (height of the triangle) and 11 cm (length of the prism):
\( A_{\text{rectangle2}} = 3 \times 11 = 33 \, \text{cm}^2 \)
- The last rectangle with dimensions 4 cm (side length of the triangle) and 11 cm (length of the prism):
\( A_{\text{rectangle3}} = 4 \times 11 = 44 \, \text{cm}^2 \)
3. **Sum of the areas of the three rectangular faces**:
\( \text{Total area of rectangles} = 55 + 33 + 44 = 132 \, \text{cm}^2 \)
4. **Total surface area of the triangular prism**:
\( \text{Total surface area} = (\text{Total area of triangular bases}) + (\text{Total area of rectangles}) \)
\( = 15 + 132 = 147 \, \text{cm}^2 \)
Therefore, the surface area of the triangular prism is \( 147 \, \text{cm}^2 \).
What is the surface area of the triangular prism?(1 point)
5cm. 3cm 11cm 4cm
1 answer
1 answer