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
2.48 cm2
2.48 cm squared
14 cm2
14 cm squared
6 cm2
6 cm squared
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page 8 of 8
To find the surface area of the triangular prism, we need to calculate the area of each individual shape in the net and add them up.
1. Each of the top and bottom rectangles have dimensions of 2.5cm by 1cm, so their area is 2.5cm * 1cm = 2.5cm^2 each. Since there are two of them, the total area for the top and bottom rectangles is 2 * 2.5cm^2 = 5cm^2.
2. The middle rectangle has dimensions of 3cm by 1cm, so its area is 3cm * 1cm = 3cm^2.
3. The two right triangles have a base of 3cm and a height of 2cm, so their area is (1/2) * base * height = (1/2) * 3cm * 2cm = 3cm^2 for each triangle. Since there are two triangles, the total area for both triangles is 2 * 3cm^2 = 6cm^2.
Adding up the areas of all the shapes:
5cm^2 (top and bottom rectangles) + 3cm^2 (middle rectangle) + 6cm^2 (triangles) = 14cm^2
Therefore, the surface area of the triangular prism is 14 cm^2.