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?
To find the surface area of the triangular prism, we need to calculate the areas of each face and then add them together.
1. The area of the triangular face:
Area = 1/2 * base * height
Area = 1/2 * 6 cm * 8 cm
Area = 24 sq cm
2. The area of the rectangular face:
Area = length * width
Area = 10 cm * 9 cm
Area = 90 sq cm
3. The area of the other rectangular face (which is the same as the one we calculated above):
Area = 90 sq cm
Now add the three areas together to get the total surface area of the triangular prism:
Total surface area = 24 sq cm + 90 sq cm + 90 sq cm
Total surface area = 204 sq cm
Therefore, the surface area of the triangular prism is 204 square centimeters.
wrong
I apologize for the mistake. Let's recalculate the surface area of the triangular prism:
1. Triangular face area:
Area = 1/2 * base * height
Area = 1/2 * 6 cm * 8 cm
Area = 24 sq cm
2. The two rectangular faces:
Each face has an area of length * width:
Face 1 area = 10 cm * 9 cm = 90 sq cm
Face 2 area = 6 cm * 8 cm = 48 sq cm
Now calculate the total surface area by adding the individual areas of the faces:
Total surface area = 24 sq cm (triangular face) + 90 sq cm (rectangular face 1) + 48 sq cm (rectangular face 2)
Total surface area = 162 sq cm
Therefore, the correct surface area of the triangular prism is 162 square centimeters.