Use the image to answer the question.
A triangular prism. The front triangular face is visible. The right rectangular face is visible. The sides and edges that are not visible are indicated by dashed lines. Parts are labeled with measurements. The left side of the triangle measures 8 centimeters. The left side meets the base to form a right angle. The base of the triangle measures 6 centimeters. The hypotenuse side of the triangle measures 10 centimeters. The width of the rectangular face measures 9 centimeters.
What is the surface area of the triangular prism?
(1 point)
square centimeters
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The surface area of the triangular prism can be calculated by summing the areas of all six faces.
1. Area of the front triangular face: 1/2 * base * height = 1/2 * 6cm * 8cm = 24 square centimeters
2. Area of the back triangular face (which is the same as the front): 24 square centimeters
3. Area of the right rectangular face: length * width = 8cm * 9cm = 72 square centimeters
4. Area of the left rectangular face (which is the same as the right): 72 square centimeters
5. Area of the top rectangular face: 6cm * 8cm = 48 square centimeters
6. Area of the bottom rectangular face (which is the same as the top): 48 square centimeters
Adding all these areas together:
24 + 24 + 72 + 72 + 48 + 48 = 288 square centimeters
Therefore, the surface area of the triangular prism is 288 square centimeters.
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I apologize for the mistake. Let's recalculate the surface area of the triangular prism.
The surface area of a triangular prism can be calculated by finding the area of each face and summing them up.
1. Front and back triangular faces: Area = 1/2 * base * height = 1/2 * 6cm * 8cm = 24 square centimeters each.
2. Top and bottom rectangular faces: Area = length * width = 6cm * 9cm = 54 square centimeters each.
3. Left and right rectangular faces: Area = width * height = 9cm * 8cm = 72 square centimeters each.
Adding all these areas together:
24 + 24 + 54 + 54 + 72 + 72 = 300 square centimeters.
Therefore, the correct surface area of the triangular prism is 300 square centimeters. Thank you for pointing out the error.
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I apologize for the mistake in my previous responses. Let me reevaluate the surface area calculation for the triangular prism.
Given:
- Front and back triangular faces: Area = 1/2 * base * height = 1/2 * 6cm * 8cm = 24 square centimeters each.
- Top and bottom rectangular faces: Area = length * width = 6cm * 9cm = 54 square centimeters each.
- Left and right rectangular faces: Area = width * height = 9cm * 8cm = 72 square centimeters each.
Now, adding all the areas together:
24 + 24 + 54 + 54 + 72 + 72 = 300 square centimeters.
Therefore, the correct surface area of the triangular prism is indeed 300 square centimeters. Thank you for your patience.