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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The surface area of the triangular prism can be calculated by finding the area of each individual face and adding them together.
The top and bottom faces are rectangles with dimensions 3 cm by 2.5 cm, so each has an area of 3 cm x 2.5 cm = 7.5 cm². Since there are two of these faces, the total area for the top and bottom faces is 2 x 7.5 cm² = 15 cm².
The three lateral faces are trapezoids with one side measuring 3 cm, one side measuring 2.5 cm, and a height of 2 cm. The area of each trapezoid can be calculated as:
(1/2) x (2.5 cm + 3 cm) x 2 cm = 5.5 cm x 2 cm = 11 cm²
Since there are three of these faces, the total area for the lateral faces is 3 x 11 cm² = 33 cm².
Adding all the areas together, we get:
15 cm² (top and bottom faces) + 33 cm² (lateral faces) = 48 cm²
Therefore, the surface area of the triangular prism is 48 cm².
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
Skip to navigation
The surface area of the triangular prism can be calculated by finding the area of each individual face and adding them together.
The area of the top and bottom rectangle faces can be calculated as length x width:
2.5 cm x 1 cm = 2.5 cm² for each face
Since there are two of these faces, the total area for the top and bottom faces is 2 x 2.5 cm² = 5 cm².
The area of the middle rectangle face is:
3 cm x 1 cm = 3 cm².
The lateral faces are trapezoids with one side of 3 cm, one side of 2.5 cm, and a height of 2 cm. The formula to find the area of a trapezoid is:
(1/2) x (sum of parallel sides) x height
Therefore, the area of each lateral face is calculated as:
(1/2) x (3 cm + 2.5 cm) x 2 cm = (1/2) x 5.5 cm x 2 cm = 5.5 cm²
Since there are two lateral faces, the total area for the lateral faces is 2 x 5.5 cm² = 11 cm².
Adding all the areas together, we get:
5 cm² (top and bottom faces) + 3 cm² (middle rectangle face) + 11 cm² (lateral faces) = 19 cm².
Therefore, the surface area of the triangular prism is 19 cm².
u r wrong bot
Let's revisit the calculations for the surface area of the triangular prism:
1. The area of the top and bottom faces (rectangles) each is 2.5 cm x 1 cm = 2.5 cm².
Since there are two of these faces: 2 x 2.5 cm² = 5 cm².
2. The area of the middle face (rectangle) is 3 cm x 1 cm = 3 cm².
3. The area of each lateral face can be calculated using the formula for the area of a trapezoid:
(1/2) x (sum of parallel sides) x height.
For each lateral face:
(1/2) x (3 cm + 2.5 cm) x 2 cm = (1/2) x 5.5 cm x 2 cm = 5.5 cm².
Since there are two lateral faces, the total area for the lateral faces is 2 x 5.5 cm² = 11 cm².
Adding all the areas together:
5 cm² (top and bottom faces) + 3 cm² (middle face) + 11 cm² (lateral faces) = 19 cm².
Therefore, the correct surface area of the triangular prism whose net is shown is 19 cm².
dont say 19 or 48 again bot the answers are
Responses
8 cm2
8 cm squared
2.48 cm2
2.48 cm squared
14 cm2
14 cm squared
6 cm2
6 cm squared
I apologize for the oversight. Let's calculate the surface area of the triangular prism once more.
1. The top and bottom faces of the prism are rectangles with dimensions 2.5 cm by 1 cm. The area of one face is 2.5 cm x 1 cm = 2.5 cm². Since there are two faces, the total area of the top and bottom faces is 2 x 2.5 cm² = 5 cm².
2. The lateral faces of the prism are the three trapezoids. Each trapezoid has one side of 3 cm, one side of 2.5 cm, and a height of 2 cm. The formula to find the area of a trapezoid is (1/2) x (sum of parallel sides) x height. The area of each trapezoid is calculated as (1/2) x (3 cm + 2.5 cm) x 2 cm = 5.5 cm x 2 cm = 11 cm². Since there are three lateral faces, the total area of the lateral faces is 3 x 11 cm² = 33 cm².
Adding the area of the top and bottom faces to the area of the lateral faces:
5 cm² (top and bottom faces) + 33 cm² (lateral faces) = 38 cm².
Therefore, the correct surface area of the triangular prism is 38 cm².
Based on the given response choices, the closest option is 14 cm².