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)
To find the surface area of the triangular prism, we need to find the area of each individual face and then add them all together.
1. Front triangular face:
Area = (1/2) * base * height
Area = (1/2) * 6 * 8
Area = 24 square centimeters
2. Right rectangular face:
Area = length * width
Area = 10 * 9
Area = 90 square centimeters
3. Left rectangular face:
This face has the same area as the right rectangular face, so it is also 90 square centimeters.
Now, add all the areas together:
Total surface area = area of front triangular face + area of right rectangular face + area of left rectangular face
Total surface area = 24 + 90 + 90
Total surface area = 204 square centimeters
Therefore, the surface area of the triangular prism is 204 square centimeters.
wrong
Apologies for the error. Let's correct the calculation for the surface area of the triangular prism:
1. Front triangular face:
Area = (1/2) * base * height
Area = (1/2) * 6 * 8
Area = 24 square centimeters
2. Right rectangular face:
Area = length * width
Area = 10 * 9
Area = 90 square centimeters
3. Left rectangular face:
This face also has an area of 90 square centimeters.
Now, we also need to consider the two side faces of the prism which are rectangles with dimensions 8 cm (height of the triangular face) and 10 cm (length of the base of the triangle). The area of each side face is:
Area = height * length
Area = 8 * 10
Area = 80 square centimeters (for each side face)
Now, add up all the areas of the faces:
Total surface area = area of front triangular face + 2*(area of right rectangular face) + 2*(area of side face)
Total surface area = 24 + 2*(90) + 2*(80)
Total surface area = 24 + 180 + 160
Total surface area = 364 square centimeters
Therefore, the correct surface area of the triangular prism is 364 square centimeters.
still wrong
I apologize for the oversight. Let's correct the calculation for the surface area of the triangular prism:
1. Front triangular face:
Area = (1/2) * base * height
Area = (1/2) * 6 * 8
Area = 24 square centimeters
2. Right rectangular face:
Area = length * width
Area = 10 * 9
Area = 90 square centimeters
3. Left rectangular face:
This face also has an area of 90 square centimeters.
Now, we also need to consider the two side faces of the prism which are rectangles with dimensions 8 cm (height of the triangular face) and 10 cm (length of the base of the triangle). The area of each side face is:
Area = height * length
Area = 8 * 10
Area = 80 square centimeters (for each side face)
Now, add up all the areas of the faces:
Total surface area = 2*(area of front triangular face) + 2*(area of right rectangular face) + 2*(area of side face)
Total surface area = 2*(24) + 2*(90) + 2*(80)
Total surface area = 48 + 180 + 160
Total surface area = 388 square centimeters
Therefore, the correct surface area of the triangular prism is 388 square centimeters.