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An illustration shows a two-dimensional net of a triangular prism with all of its sides open and visible. The net appears as three horizontal rectangles joined next to each other. All 4 sides of the middle rectangle are drawn with dashed lines. The width of the 3 rectangles is 1 centimeter. The length of the outer rectangles is 2.5 centimeters. The length of the middle rectangle is 3 centimeters. Two right triangles adjoin the middle rectangle on the top and bottom along the 3 centimeter side, with their perpendicular height measuring 2 centimeters. A right angle is shown where the perpendicular height intersects with the triangle base.

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

(1 point)
Responses

14 cm2
14 cm squared

6 cm2
6 cm squared

8 cm2
8 cm squared

2.48 cm2

1 answer

To find the surface area of the triangular prism, we need to calculate the areas of all the faces represented in the net.

  1. Area of the two triangular bases: Each triangular base is a right triangle with:

    • Base = 1 cm (width of the triangles)
    • Height = 2 cm (perpendicular height)

    The area of one triangular base = (1/2) * base * height = (1/2) * 1 cm * 2 cm = 1 cm². Since there are two triangular bases: Total area of the triangular bases = 2 * 1 cm² = 2 cm².

  2. Area of the three rectangular sides: The three rectangles have the following dimensions:

    • Two outer rectangles (length = 2.5 cm, width = 1 cm): Area of one outer rectangle = length * width = 2.5 cm * 1 cm = 2.5 cm². Total area for the two outer rectangles = 2 * 2.5 cm² = 5 cm².

    • One middle rectangle (length = 3 cm, width = 1 cm): Area of the middle rectangle = length * width = 3 cm * 1 cm = 3 cm².

    Total area of the rectangular sides = Area of outer rectangles + Area of middle rectangle = 5 cm² + 3 cm² = 8 cm².

  3. Total surface area of the prism: Total surface area = Area of triangular bases + Area of rectangular sides = 2 cm² + 8 cm² = 10 cm².

The closest option in the responses provided is not available, but based on the calculations, the surface area of the triangular prism is 10 cm². If the only choices are those listed:

  • 14 cm²
  • 6 cm²
  • 8 cm²
  • 2.48 cm²

None of these match the calculated surface area.

Please review the options or provide additional information.