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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
Remaining Attempts : 3

1 answer

To calculate the surface area of the net of a triangular prism, we need to sum up the areas of the rectangles and the triangles in the net.

  1. Identify the dimensions:

    • The dimensions of the rectangles:
      • Length (top and bottom rectangles): 10 cm
      • Width (top and bottom rectangles): 5 cm
    • The dimensions of the triangles:
      • Base: 5 cm
      • Height: 4 cm

  2. Calculate the areas of the rectangles:

    • Area of the top rectangle = Length × Width = 10 cm × 5 cm = 50 cm²
    • Area of the bottom rectangle = Length × Width = 10 cm × 5 cm = 50 cm²
    • Area of the middle rectangle (the height of the prism is not given, but let's assume it is equal to the height of the triangle, which is 4 cm):
      • Area = Length × Height = 10 cm × 4 cm = 40 cm²

  3. Calculate the area of the triangles:

    • Area of one triangle = (1/2) × Base × Height = (1/2) × 5 cm × 4 cm = 10 cm²
    • Since there are two identical triangles, the total area for both triangles is:
      • Total area of triangles = 2 × 10 cm² = 20 cm²

  4. Add all areas together:

    • Total surface area = Area of top rectangle + Area of bottom rectangle + Area of middle rectangle + Area of triangles
    • Total surface area = 50 cm² + 50 cm² + 40 cm² + 20 cm² = 160 cm²

Therefore, the surface area of the net of the triangular prism is 160 square centimeters.