Use the image to answer the question.

Question

An illustration shows a two-dimensional net of a triangular prism with all of its sides open and visible. The net appears as three vertical rectangles joined one on top of the other. All 4 sides of the middle rectangle are drawn with dashed lines. The width of the rectangles is 7 millimeters. The length of the middle rectangle is 8 millimeters. Two right triangles adjoin the middle rectangle on the left and the right, with the perpendicular sides measuring 6 millimeters and the hypotenuse measuring 10 millimeters.

Using the net of the prism shown, what is its surface area?

(1 point)
mm2

Answer 1

To calculate the surface area of the triangular prism, we can break it down into the areas of the rectangles and the triangles in the net.

Given Dimensions:

• Width of the rectangles (prism) = 7 mm
• Length of the middle rectangle (height, h) = 8 mm
• Perpendicular sides of the right triangles = 6 mm (base) and 6 mm (height)
• Area of the triangular base = (1/2) * base * height = (1/2) * 6 mm * 6 mm = 18 mm²

Calculate the Areas:

1. Area of the three rectangles:

   • Each of the vertical rectangles on the sides has a length (height of the prism) of 8 mm and a width of 7 mm.
   • Area of one rectangle = width * height = 7 mm * 8 mm = 56 mm²
   • Since there are 3 rectangles:
     • Total area of rectangles = 3 * 56 mm² = 168 mm²

2. Area of the two triangular bases:

   • Each triangular base has an area of 18 mm² (calculated above).
   • Total area of the triangles = 2 * 18 mm² = 36 mm²

Total Surface Area:

• Total Surface Area (SA) = Area of rectangles + Area of triangles
• Total Surface Area = 168 mm² + 36 mm² = 204 mm²

Thus, the surface area of the triangular prism is 204 mm².