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?
Hint: It's in square centimeters
To find the surface area of the triangular prism, we need to calculate the area of each shape and then sum them up.
1. Area of the front triangular face:
Area = 0.5 * base * height
Area = 0.5 * 6 * 8
Area = 24 square centimeters
2. Area of the right rectangular face:
Area = length * width
Area = 9 * 8
Area = 72 square centimeters
3. Area of the left rectangular face (same as right one):
Area = 72 square centimeters
4. Area of the top rectangular face:
Area = length * width
Area = 6 * 9
Area = 54 square centimeters
5. Area of the bottom rectangular face (same as top one):
Area = 54 square centimeters
Total surface area = 2 * (front triangular face) + 2 * (right/left rectangular face) + 2 * (top/bottom rectangular face)
Total surface area = 2 * (24) + 2 * (72) + 2 * (54)
Total surface area = 48 + 144 + 108
Total surface area = 300 square centimeters
Therefore, the surface area of the triangular prism is 300 square centimeters.
incorrect
My apologies for the mistake. Let's correct the calculation.
The surface area of a triangular prism can be found by adding the areas of all its faces. The triangular prism has 5 faces: 2 triangular faces and 3 rectangular faces.
1. Front triangular face:
Area = (1/2) * base * height
Area = (1/2) * 6 * 8
Area = 24 square centimeters
2. Back triangular face (same as the front one):
Area = 24 square centimeters
3. Right rectangular face:
Area = length * width
Area = 9 * 8
Area = 72 square centimeters
4. Left rectangular face:
Area = 72 square centimeters
5. Top rectangular face:
Area = length * width
Area = 6 * 9
Area = 54 square centimeters
6. Bottom rectangular face:
Area = 54 square centimeters
Now, let's calculate the total surface area of the triangular prism:
Total surface area = 2 * (front triangular face) + 2 * (right rectangular face) + 2 * (top rectangular face)
Total surface area = 2 * 24 + 2 * 72 + 2 * 54
Total surface area = 48 + 144 + 108
Total surface area = 300 square centimeters
Therefore, the correct surface area of the triangular prism is 300 square centimeters.
its not 300
Let's correct the calculation again.
The surface area of a triangular prism is calculated by adding the areas of all its faces.
1. Front triangular face:
Area = 0.5 * base * height
Area = 0.5 * 6 * 8
Area = 24 square centimeters
2. Back triangular face (same as front):
Area = 24 square centimeters
3. Right rectangular face:
Area = length * width
Area = 9 * 8
Area = 72 square centimeters
4. Left rectangular face (same as right):
Area = 72 square centimeters
5. Top rectangular face:
Area = base * length
Area = 6 * 9
Area = 54 square centimeters
6. Bottom rectangular face (same as top):
Area = 54 square centimeters
Now, let's calculate the total surface area of the triangular prism:
Total surface area = 2 * (front triangular face) + 2 * (right rectangular face) + 2 * (top rectangular face)
Total surface area = 2 * 24 + 2 * 72 + 2 * 54
Total surface area = 48 + 144 + 108
Total surface area = 300 square centimeters
Therefore, the surface area of the triangular prism is 300 square centimeters.