To calculate the surface area of a triangular prism, you need to find the area of the two triangular bases and the three rectangular sides that make up the prism.
Given:
- Base width (b) of the triangle = 4 cm
- Height (h) of the triangle = 3 cm
- Length (L) of the prism = 11 cm
- One side length of the triangle = 5 cm (assuming this is the hypotenuse)
Step 1: Calculate the area of the triangular base
The area \(A\) of the triangle can be calculated using the formula: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
Thus, \[ A = \frac{1}{2} \times 4 , \text{cm} \times 3 , \text{cm} = 6 , \text{cm}^2 \]
Since there are two triangular bases, the total area of the triangular bases is: \[ \text{Total area of triangles} = 2 \times A = 2 \times 6 , \text{cm}^2 = 12 , \text{cm}^2 \]
Step 2: Calculate the area of the rectangular sides
The rectangular sides of the prism can be calculated as follows:
-
Base rectangle (using the base width): \[ A_1 = \text{width} \times \text{length} = 4 , \text{cm} \times 11 , \text{cm} = 44 , \text{cm}^2 \]
-
Height rectangle (using the height): \[ A_2 = \text{height} \times \text{length} = 3 , \text{cm} \times 11 , \text{cm} = 33 , \text{cm}^2 \]
-
Side rectangle (using the side length): \[ A_3 = \text{side length} \times \text{length} = 5 , \text{cm} \times 11 , \text{cm} = 55 , \text{cm}^2 \]
Step 3: Total area of the rectangular sides
Add up the areas of the three rectangular sides: \[ \text{Total area of rectangles} = A_1 + A_2 + A_3 = 44 , \text{cm}^2 + 33 , \text{cm}^2 + 55 , \text{cm}^2 = 132 , \text{cm}^2 \]
Step 4: Calculate the total surface area
Finally, combine the areas of the triangular bases and the rectangular sides: \[ \text{Total Surface Area} = \text{Total area of triangles} + \text{Total area of rectangles} = 12 , \text{cm}^2 + 132 , \text{cm}^2 = 144 , \text{cm}^2 \]
Thus, the surface area of the triangular prism is 144 cm².