Use the image to answer the question.
An illustration shows a triangular prism. The front triangular face is visible. The left rectangular face is visible. The sides and edges that are not visible are indicated by dashed lines. Parts are labeled with measurements. All sides of the triangle measure 10 centimeters. The perpendicular height from the top vertex of the triangle to the base measures 8 centimeters. The width of the rectangular face measures 6 centimeters.
Solve for the surface area of the triangular prism.
(1 point)
Responses
180 square centimeters
180 square centimeters
280 square centimeters
280 square centimeters
320 square centimeters
320 square centimeters
260 square centimeters
260 square centimeters
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To find the surface area of the triangular prism, we need to calculate the areas of all the faces and then add them together.
The front triangular face has a base of 10 cm and a height of 8 cm, so its area is (1/2) * base * height = (1/2) * 10 * 8 = 40 square cm.
There are two rectangular faces, each with a length of 10 cm and a width of 6 cm, so the area of one rectangular face is length * width = 10 * 6 = 60 square cm. Since there are two rectangular faces, the total area for both is 2 * 60 = 120 square cm.
Adding all the areas together, we have: 40 (front triangle) + 120 (both rectangular faces) = 160 square cm.
Therefore, the surface area of the triangular prism is 160 square centimeters.
mmmmm no
I apologize for the mistake in my previous response. Let's try solving it again.
The surface area of a triangular prism is calculated by adding the areas of all its faces.
First, let's find the area of the triangular face. Since it is an isosceles triangle, the area can be calculated using the formula: (1/2) * base * height, where the base is 10 cm and the height is 8 cm.
Area of the triangular face = (1/2) * 10 * 8 = 40 square cm
Next, let's find the area of the rectangular faces. Each rectangular face has a length of 10 cm and a width of 6 cm.
Area of one rectangular face = length * width = 10 * 6 = 60 square cm
Since there are two rectangular faces, the total area for both is: 2 * 60 = 120 square cm
Now, add all the areas together to find the total surface area of the triangular prism:
Total surface area = 40 (triangle) + 120 (both rectangles) = 160 square cm
Therefore, the correct surface area of the triangular prism is 160 square centimeters.
nnoooo
I apologize for the mistake in my previous responses. Let's calculated the surface area of the triangular prism correctly this time.
The surface area of a triangular prism can be calculated by adding the areas of all its faces.
1. Front triangular face:
The area of the front triangular face can be calculated as (1/2) * base * height, where the base is 10 cm and the height is 8 cm.
Area of the front triangular face = (1/2) * 10 * 8 = 40 square cm
2. Back triangular face (which is congruent to the front triangular face):
Since the back triangular face is identical to the front triangular face, its area is also 40 square cm.
3. Two rectangular faces:
Each rectangular face has a length of 10 cm and a width of 6 cm.
Area of one rectangular face = length * width = 10 * 6 = 60 square cm
Since there are two rectangular faces, the total area for both is: 2 * 60 = 120 square cm
Now, add all the areas together to find the total surface area of the triangular prism:
Total surface area = 40 (front triangle) + 40 (back triangle) + 120 (both rectangles) = 200 square cm
Therefore, the correct surface area of the triangular prism is 200 square centimeters. Thank you for pointing out the error.
the answer that you're saying is wrong its only 180 280 320 260
Apologies for the errors in my previous responses. Let's reevaluate the calculation correctly this time.
The surface area of a triangular prism consists of the two triangular faces and three rectangular faces.
1. Front and Back Triangular Faces:
Area of a triangle = (1/2) * base * height
Area of each triangular face = (1/2) * 10 * 8 = 40 square cm
Since there are two identical triangular faces, the total area for both is: 2 * 40 = 80 square cm
2. Three Rectangular Faces:
Each rectangular face has dimensions of 10 cm by 6 cm.
Area of one rectangular face = 10 * 6 = 60 square cm
Since there are three rectangular faces, the total area for all three is: 3 * 60 = 180 square cm
Now, add all the areas together to find the total surface area of the triangular prism:
Total surface area = 80 (triangular faces) + 180 (rectangular faces) = 260 square cm
Therefore, the correct surface area of the triangular prism is 260 square centimeters. Thank you for your patience.