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An illustration shows a net version of a triangular prism. The net model shows 3 rectangles top to bottom. Identical triangles are attached to the left and right of the middle rectangle. Parts are labeled with measurements. The top and bottom rectangles have a length measuring 10 centimeters and a width measuring 5 centimeters. The perpendicular height from the top vertex of the triangle to the base measures 4 centimeters. The base of the triangle measures 5 centimeters. The base shares an edge with the middle rectangle.

What is the surface area of the net of the triangular prism?

(1 point)
square centimeters

1 answer

To find the surface area of the net of the triangular prism, we need to calculate the area of all the faces (rectangles and triangles) of the prism.

  1. Areas of Rectangles:

    • There are three rectangles:
      • Top rectangle: Length = 10 cm, Width = 5 cm
      • Middle rectangle: Length = 10 cm, Width = 5 cm
      • Bottom rectangle: Length = 10 cm, Width = 5 cm

    Each rectangle has an area calculated as: \[ \text{Area of one rectangle} = \text{Length} \times \text{Width} = 10 , \text{cm} \times 5 , \text{cm} = 50 , \text{cm}^2 \]

    Since there are three rectangles, the total area of the rectangles is: \[ \text{Total area of rectangles} = 3 \times 50 , \text{cm}^2 = 150 , \text{cm}^2 \]

  2. Areas of Triangles:

    • There are two identical triangles.
    • Base of the triangle = 5 cm
    • Height of the triangle = 4 cm

    The area of one triangle is calculated as: \[ \text{Area of one triangle} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 5 , \text{cm} \times 4 , \text{cm} = 10 , \text{cm}^2 \]

    Since there are two triangles, the total area of the triangles is: \[ \text{Total area of triangles} = 2 \times 10 , \text{cm}^2 = 20 , \text{cm}^2 \]

  3. Total Surface Area:

    • Now, we add the total area of the rectangles and the total area of the triangles to get the surface area of the prism: \[ \text{Total Surface Area} = \text{Total area of rectangles} + \text{Total area of triangles} = 150 , \text{cm}^2 + 20 , \text{cm}^2 = 170 , \text{cm}^2 \]

So, the surface area of the net of the triangular prism is 170 square centimeters.