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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

6 cm2
6 cm squared

14 cm2
14 cm squared

8 cm2
8 cm squared

2.48 cm2
2.48 cm squared
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Answer 1

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

1. Identify the components:

   • There are 3 rectangular faces (two outer rectangles and one middle rectangle).
   • Two triangular faces are formed by the right triangles at the top and bottom of the middle rectangle.

2. Calculate the area of the rectangular faces:

   • Area of each outer rectangle (2.5 cm length x 1 cm width): \[ \text{Area} = 2.5 , \text{cm} \times 1 , \text{cm} = 2.5 , \text{cm}^2 \]
   • Since there are 2 outer rectangles: \[ \text{Total area of outer rectangles} = 2 \times 2.5 , \text{cm}^2 = 5 , \text{cm}^2 \]
   • Area of the middle rectangle (3 cm length x 1 cm width): \[ \text{Area} = 3 , \text{cm} \times 1 , \text{cm} = 3 , \text{cm}^2 \]

3. Calculate the area of the triangular faces:

   • Each triangular face is a right triangle with a base of 1 cm (since the bottom of the triangle is the rectangle's width) and a height of 2 cm. The area of one triangle: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 1 , \text{cm} \times 2 , \text{cm} = 1 , \text{cm}^2 \]
   • Since there are 2 triangular faces: \[ \text{Total area of triangular faces} = 2 \times 1 , \text{cm}^2 = 2 , \text{cm}^2 \]

4. Combine all areas to find the total surface area: \[ \text{Total Surface Area} = 5 , \text{cm}^2 + 3 , \text{cm}^2 + 2 , \text{cm}^2 = 10 , \text{cm}^2 \]

Given the choices, it looks like the answer 10 cm² is not listed in the options, leading us to a possible oversight in calculations from the provided options.

Verify the closest provided option:

• 6 cm²: Less than calculated surface area.
• 14 cm²: More than calculated surface area.
• 8 cm²: Less than calculated surface area.
• 2.48 cm²: Much less.

It appears there might be a mistake. However, if forced to choose from the options, 14 cm² would be selected as it is closest to providing a greater estimate than 10 cm².

Please double-check the given measurements and text to ensure accuracy or clarify any discrepancies.