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 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

14 cm2
14 cm squared

2.48 cm2
2.48 cm squared

6 cm2
6 cm squared

8 cm2

Answer 1

To find the surface area of the triangular prism shown in the net, we need to calculate the area of all the shapes visible in the net.

1. Areas of the rectangular faces:

   • There are three rectangles:

     • Two outer rectangles (2.5 cm length, 1 cm width each): \[ \text{Area of one outer rectangle} = \text{length} \times \text{width} = 2.5 , \text{cm} \times 1 , \text{cm} = 2.5 , \text{cm}^2 \] \[ \text{Total area for both outer rectangles} = 2 \times 2.5 , \text{cm}^2 = 5 , \text{cm}^2 \]
     • One middle rectangle (3 cm length, 1 cm width): \[ \text{Area of middle rectangle} = 3 , \text{cm} \times 1 , \text{cm} = 3 , \text{cm}^2 \]

   • Total area of rectangles: \[ 5 , \text{cm}^2 + 3 , \text{cm}^2 = 8 , \text{cm}^2 \]

2. Areas of the triangular faces:

   • There are two right triangles at the ends of the prism:
     • Each triangle has a base (the length of the triangle) which is 1 cm (width of the prism) and height of 2 cm: \[ \text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 1 , \text{cm} \times 2 , \text{cm} = 1 , \text{cm}^2 \]
     • Total area for two triangles: \[ 2 \times 1 , \text{cm}^2 = 2 , \text{cm}^2 \]

3. Total Surface Area:

   • Adding the area from the rectangular faces and triangular faces: \[ \text{Total Surface Area} = \text{Area of rectangles} + \text{Area of triangles} = 8 , \text{cm}^2 + 2 , \text{cm}^2 = 10 , \text{cm}^2 \]

Therefore, the surface area of the triangular prism is \(10 , \text{cm}^2\). However, this option is not one of the provided responses. It seems there was an error in the options presented or in the calculations. Based on the calculations, the surface area should be reported as 10 cm², even though the closest possible answer in the options provided may have been meant to round to the nearest or be included incorrectly.

Should the calculation instead yield a surface area in accordance with given choices, please double-check for any errors in interpretation from the question or visual representation details accounted.