To find the surface area of the triangular prism, we will calculate the area of all the faces in the net.
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Identify the dimensions:
- The top and bottom rectangles each have a length of 10 cm and a width of 5 cm.
- The middle rectangle (the lateral face) has a length of 10 cm and a height of 5 cm.
- The triangular faces have a base of 5 cm and a height of 4 cm.
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Calculate the area of the rectangles:
- Top rectangle: \[ \text{Area} = \text{length} \times \text{width} = 10 , \text{cm} \times 5 , \text{cm} = 50 , \text{cm}^2 \]
- Bottom rectangle: \[ \text{Area} = 10 , \text{cm} \times 5 , \text{cm} = 50 , \text{cm}^2 \]
- Middle rectangle (lateral face): \[ \text{Area} = 10 , \text{cm} \times 5 , \text{cm} = 50 , \text{cm}^2 \]
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Calculate the area of the triangular faces:
- Area of one triangle using the formula \(\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}\): \[ \text{Area} = \frac{1}{2} \times 5 , \text{cm} \times 4 , \text{cm} = \frac{1}{2} \times 20 , \text{cm}^2 = 10 , \text{cm}^2 \]
- Since there are two identical triangular faces, the total area of both triangles is: \[ 2 \times 10 , \text{cm}^2 = 20 , \text{cm}^2 \]
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Total surface area of the prism: \[ \text{Total Surface Area} = \text{Area of top rectangle} + \text{Area of bottom rectangle} + \text{Area of lateral rectangle} + \text{Area of triangles} \] \[ = 50 , \text{cm}^2 + 50 , \text{cm}^2 + 50 , \text{cm}^2 + 20 , \text{cm}^2 = 220 , \text{cm}^2 \]
So the surface area of the net of the triangular prism is 220 square centimeters.