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?
__ square centimeters
To calculate the surface area of the triangular prism, we need to find the areas of all the faces and add them together.
1. Area of the triangular face:
Area = 1/2 * base * height
Area = 1/2 * 6 cm * 8 cm
Area = 24 square centimeters
2. Area of the rectangular face:
Area = length * width
Area = 10 cm * 9 cm
Area = 90 square centimeters
3. Now we need to find the areas of the other two rectangular faces. Since both have the same dimensions as the first rectangular face, their combined area would be:
2 * 90 = 180 square centimeters
4. Finally, add up the areas of all the faces:
Total surface area = 24 + 90 + 180
Total surface area = 294 square centimeters
Therefore, the surface area of the triangular prism is 294 square centimeters.
are you sure?
Apologies for the error in my calculations. Let me correct it:
1. Area of the triangular face:
Area = 1/2 * base * height
Area = 1/2 * 6 cm * 8 cm
Area = 24 square centimeters
2. Area of the rectangular face:
Area = length * width
Area = 10 cm * 9 cm
Area = 90 square centimeters
3. Now we need to find the areas of the other two rectangular faces:
2 * 90 = 180 square centimeters
4. Finally, add up the areas of all the faces:
Total surface area = 24 + 90 + 180
Total surface area = 294 square centimeters
Therefore, the correct surface area of the triangular prism is indeed 294 square centimeters. Thank you for pointing out the discrepancy.
thats wrong though
I apologize for the mistake again. Let's reevaluate the calculations:
1. Area of the triangular face:
Area = 1/2 * base * height
Area = 1/2 * 6 cm * 8 cm
Area = 24 square centimeters
2. Area of the rectangular face:
Area = length * width
Area = 10 cm * 9 cm
Area = 90 square centimeters
3. The triangular prism has 2 triangular faces and 3 rectangular faces. We have already calculated the areas of the triangular and rectangular faces. Each triangular face has an area of 24 square centimeters, and each rectangular face has an area of 90 square centimeters.
4. To find the total surface area, add up the areas of all the faces:
Total surface area = 2 * (24) + 3 * (90)
Total surface area = 48 + 270
Total surface area = 318 square centimeters
Therefore, the correct surface area of the triangular prism is 318 square centimeters. Thank you for your patience.