Use the image to answer the 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 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
8 cm2
8 cm squared
6 cm2
6 cm squared
14 cm2
14 cm squared
2.48 cm2
2.48 cm squared
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The surface area of the triangular prism is 14 cm squared.
To calculate the surface area of a triangular prism, we need to find the area of all the individual faces and then add them up.
The rectangular faces have an area of 2.5 cm x 1 cm = 2.5 cm² each, so for the two rectangular faces, the total area is 2 * 2.5 cm² = 5 cm².
The triangular faces have an area of 1/2 * base * height, so for each triangular face, the area is 1/2 * 3 cm * 2 cm = 3 cm².
The total area for both triangular faces is 2 * 3 cm² = 6 cm².
Adding the total areas of the rectangular faces (5 cm²) and the triangular faces (6 cm²) gives us a total surface area of 5 cm² + 6 cm² = 11 cm².
Therefore, the surface area of the triangular prism is 11 cm².