To find the surface area of the triangular prism, we need to find the area of each face and then add them all together.
1. The triangular faces:
- The base of the triangular prism is a right triangle with side lengths of 10 cm and 24 cm. The area of a right triangle is (1/2) * base * height. So, the area of each triangular face is:
(1/2) * 10 cm * 24 cm = 120 cm²
Since there are two triangular faces, the total area for the triangular faces is:
2 * 120 cm² = 240 cm²
2. The rectangular faces:
- The rectangular face on the top of the prism has the dimensions of 10 cm by 24 cm, giving an area of:
10 cm * 24 cm = 240 cm²
- The rectangular face on the bottom of the prism also has an area of 240 cm².
Adding the areas of all faces together:
240 cm² (triangular faces) + 240 cm² (top rectangular face) + 240 cm² (bottom rectangular face) = 720 cm²
Therefore, the surface area of the triangular prism is 720 cm².
Use the image to answer the question.
What is the surface area of the triangular prism? Round the answer to the nearest tenth. (1 point)
cm 2
7 answers
Wrong
I apologize for the error in my previous response. Let's calculate the surface area correctly using the image.
Surface area of a triangular prism can be calculated by finding the areas of all the individual faces and adding them together.
1. The two triangular faces:
- The base of the prism is a right triangle with base 10 cm and height 24 cm. The area of a triangle is (1/2) * base * height. So, the area of each triangular face is:
(1/2) * 10 cm * 24 cm = 120 cm²
Since there are two triangular faces, the total area for the triangular faces is:
2 * 120 cm² = 240 cm²
2. The three rectangular faces:
- The two rectangular faces on the sides of the prism have dimensions of 10 cm by 12 cm each. The area of each rectangular face is:
10 cm * 12 cm = 120 cm²
- The rectangular face on the top of the prism has dimensions of 24 cm by 12 cm, giving an area of:
24 cm * 12 cm = 288 cm²
Adding the areas of all faces together:
240 cm² (triangular faces) + 120 cm² (side rectangular faces) + 120 cm² (side rectangular faces) + 288 cm² (top rectangular face) = 768 cm²
Therefore, the correct surface area of the triangular prism is 768 cm². Thank you for pointing out the error.
Surface area of a triangular prism can be calculated by finding the areas of all the individual faces and adding them together.
1. The two triangular faces:
- The base of the prism is a right triangle with base 10 cm and height 24 cm. The area of a triangle is (1/2) * base * height. So, the area of each triangular face is:
(1/2) * 10 cm * 24 cm = 120 cm²
Since there are two triangular faces, the total area for the triangular faces is:
2 * 120 cm² = 240 cm²
2. The three rectangular faces:
- The two rectangular faces on the sides of the prism have dimensions of 10 cm by 12 cm each. The area of each rectangular face is:
10 cm * 12 cm = 120 cm²
- The rectangular face on the top of the prism has dimensions of 24 cm by 12 cm, giving an area of:
24 cm * 12 cm = 288 cm²
Adding the areas of all faces together:
240 cm² (triangular faces) + 120 cm² (side rectangular faces) + 120 cm² (side rectangular faces) + 288 cm² (top rectangular face) = 768 cm²
Therefore, the correct surface area of the triangular prism is 768 cm². Thank you for pointing out the error.
Still wrong.....
I apologize for the mistakes in my previous responses. Let's calculate the surface area of the triangular prism correctly using the image given.
To find the surface area of the triangular prism, we need to calculate the area of all the faces and then add them together.
1. Triangular face:
- The triangular face on each end of the prism is a right triangle with base 10 cm and height 24 cm. The area of a triangle is (1/2) * base * height.
Area of one triangular face = (1/2) * 10 cm * 24 cm = 120 cm² (for each end)
Since there are two ends, the total area for the triangular ends = 2 * 120 cm² = 240 cm²
2. Rectangular faces:
- The three rectangular faces are all rectangles with dimensions:
- Top and bottom faces: 10 cm by 24 cm
- Side face: 10 cm by 12 cm (since the slant height is 12 cm)
The area of a rectangle is length * width.
Area of top and bottom faces = 10 cm * 24 cm = 240 cm² (each)
Area of side face = 10 cm * 12 cm = 120 cm²
Total area for the three rectangular faces = 2 * 240 cm² + 120 cm² = 600 cm²
Adding the areas of all faces together:
240 cm² (triangular faces) + 600 cm² (rectangular faces) = 840 cm²
Therefore, the correct surface area of the triangular prism is 840 cm². Thank you for your patience.
To find the surface area of the triangular prism, we need to calculate the area of all the faces and then add them together.
1. Triangular face:
- The triangular face on each end of the prism is a right triangle with base 10 cm and height 24 cm. The area of a triangle is (1/2) * base * height.
Area of one triangular face = (1/2) * 10 cm * 24 cm = 120 cm² (for each end)
Since there are two ends, the total area for the triangular ends = 2 * 120 cm² = 240 cm²
2. Rectangular faces:
- The three rectangular faces are all rectangles with dimensions:
- Top and bottom faces: 10 cm by 24 cm
- Side face: 10 cm by 12 cm (since the slant height is 12 cm)
The area of a rectangle is length * width.
Area of top and bottom faces = 10 cm * 24 cm = 240 cm² (each)
Area of side face = 10 cm * 12 cm = 120 cm²
Total area for the three rectangular faces = 2 * 240 cm² + 120 cm² = 600 cm²
Adding the areas of all faces together:
240 cm² (triangular faces) + 600 cm² (rectangular faces) = 840 cm²
Therefore, the correct surface area of the triangular prism is 840 cm². Thank you for your patience.
If this was a real test you would have made me fail my test...
I apologize for the errors in my responses. Thank you for your patience and understanding. It is important to provide accurate information, especially when helping with educational questions or assessments. If you have any more questions or need further clarification on any topic, please feel free to ask. Thank you for bringing this to my attention.