Question
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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)
square centimeters
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)
square centimeters
Answers
Answer
the answer is not 204
Answer
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An illustration shows a net version of a triangular prism. The net model shows 3 rectangles top to bottom. Identical triangles are attached to the left and right of the middle rectangle. Parts are labeled with measurements. The top and bottom rectangles have a length measuring 10 centimeters and a width measuring 5 centimeters. The perpendicular height from the top vertex of the triangle to the base measures 4 centimeters. The base of the triangle measures 5 centimeters. The base shares an edge with the middle rectangle.
What is the surface area of the net of the triangular prism?
An illustration shows a net version of a triangular prism. The net model shows 3 rectangles top to bottom. Identical triangles are attached to the left and right of the middle rectangle. Parts are labeled with measurements. The top and bottom rectangles have a length measuring 10 centimeters and a width measuring 5 centimeters. The perpendicular height from the top vertex of the triangle to the base measures 4 centimeters. The base of the triangle measures 5 centimeters. The base shares an edge with the middle rectangle.
What is the surface area of the net of the triangular prism?
Answer
the answer is not 140
Answered by
GPT 3.5
The surface area of a triangular prism is calculated by finding the sum of the areas of all of its faces.
The front triangular face has an area of (1/2) * base * height = (1/2) * 6 * 8 = 24 square centimeters.
The two rectangular faces have an area of length * width = 10 * 9 = 90 square centimeters each. Since there are two rectangular faces, the total area of both is 90 * 2 = 180 square centimeters.
Adding the area of the front triangular face to the total area of the two rectangular faces, the surface area of the triangular prism is 24 + 180 = 204 square centimeters.
The front triangular face has an area of (1/2) * base * height = (1/2) * 6 * 8 = 24 square centimeters.
The two rectangular faces have an area of length * width = 10 * 9 = 90 square centimeters each. Since there are two rectangular faces, the total area of both is 90 * 2 = 180 square centimeters.
Adding the area of the front triangular face to the total area of the two rectangular faces, the surface area of the triangular prism is 24 + 180 = 204 square centimeters.
Answered by
GPT 3.5
I apologize for the mistake. Let's correct the calculations.
The total surface area of a triangular prism is given by the formula:
Total Surface Area = 2 * (Area of Front Triangular Face) + (Perimeter of the Base * Height of the Prism)
First, let's find the area of the front triangular face:
Area of Front Triangular Face = (1/2) * base * height
Area of Front Triangular Face = (1/2) * 6 * 8
Area of Front Triangular Face = 24 square centimeters
Next, let's find the perimeter of the base (since the base is a right-angled triangle, the perimeter is the sum of all sides):
Perimeter of Base = 6 + 8 + 10
Perimeter of Base = 24 centimeters
Now we can calculate the total surface area:
Total Surface Area = 2 * 24 + 24 * 9
Total Surface Area = 48 + 216
Total Surface Area = 264 square centimeters
Therefore, the correct surface area of the triangular prism is 264 square centimeters.
The total surface area of a triangular prism is given by the formula:
Total Surface Area = 2 * (Area of Front Triangular Face) + (Perimeter of the Base * Height of the Prism)
First, let's find the area of the front triangular face:
Area of Front Triangular Face = (1/2) * base * height
Area of Front Triangular Face = (1/2) * 6 * 8
Area of Front Triangular Face = 24 square centimeters
Next, let's find the perimeter of the base (since the base is a right-angled triangle, the perimeter is the sum of all sides):
Perimeter of Base = 6 + 8 + 10
Perimeter of Base = 24 centimeters
Now we can calculate the total surface area:
Total Surface Area = 2 * 24 + 24 * 9
Total Surface Area = 48 + 216
Total Surface Area = 264 square centimeters
Therefore, the correct surface area of the triangular prism is 264 square centimeters.
Answered by
GPT 3.5
To find the surface area of the net of the triangular prism, we need to calculate the area of each individual shape and then sum them up.
1. The top and bottom rectangles:
- Area of each rectangle = length * width = 10 * 5 = 50 square centimeters
- Since there are two identical rectangles, the total area for both is 50 * 2 = 100 square centimeters.
2. The middle rectangle:
- The middle rectangle shares an edge with the base of the triangle, so the height of the middle rectangle is the same as the height of the triangle, which is 4 centimeters.
- The length of the middle rectangle is the same as the base of the top and bottom rectangles, which is 5 centimeters.
- Area of the middle rectangle = length * height = 5 * 4 = 20 square centimeters.
3. The two triangles:
- The two triangles are identical right triangles with a base of 5 centimeters and a height of 4 centimeters.
- Area of each triangle = (1/2) * base * height = (1/2) * 5 * 4 = 10 square centimeters
- Since there are two identical triangles, the total area for both is 10 * 2 = 20 square centimeters.
Now, sum up the areas of all the shapes:
Total surface area = 100 (top and bottom rectangles) + 20 (middle rectangle) + 20 (two triangles) = 140 square centimeters.
Therefore, the surface area of the net of the triangular prism is 140 square centimeters.
1. The top and bottom rectangles:
- Area of each rectangle = length * width = 10 * 5 = 50 square centimeters
- Since there are two identical rectangles, the total area for both is 50 * 2 = 100 square centimeters.
2. The middle rectangle:
- The middle rectangle shares an edge with the base of the triangle, so the height of the middle rectangle is the same as the height of the triangle, which is 4 centimeters.
- The length of the middle rectangle is the same as the base of the top and bottom rectangles, which is 5 centimeters.
- Area of the middle rectangle = length * height = 5 * 4 = 20 square centimeters.
3. The two triangles:
- The two triangles are identical right triangles with a base of 5 centimeters and a height of 4 centimeters.
- Area of each triangle = (1/2) * base * height = (1/2) * 5 * 4 = 10 square centimeters
- Since there are two identical triangles, the total area for both is 10 * 2 = 20 square centimeters.
Now, sum up the areas of all the shapes:
Total surface area = 100 (top and bottom rectangles) + 20 (middle rectangle) + 20 (two triangles) = 140 square centimeters.
Therefore, the surface area of the net of the triangular prism is 140 square centimeters.
Answered by
GPT 3.5
I apologize for the miscalculation. Let's correct the calculations:
The surface area of the net of the triangular prism can be found by calculating the area of each individual shape and then summing them up.
1. Top and Bottom Rectangles:
- Area of each rectangle = length * width = 10 * 5 = 50 square centimeters
- Since there are two identical rectangles (top and bottom), the total area for both is 50 * 2 = 100 square centimeters.
2. Middle Rectangle:
- The middle rectangle shares an edge with the base of the triangle, so it has the same dimensions as the top and bottom rectangles.
- Area of the middle rectangle = length * width = 10 * 5 = 50 square centimeters.
3. Two Triangles:
- Area of each triangle = (1/2) * base * height = (1/2) * 5 * 4 = 10 square centimeters
- Since there are two identical triangles, the total area for both is 10 * 2 = 20 square centimeters.
Now, sum up the areas of all the shapes:
Total surface area = 100 (top and bottom rectangles) + 50 (middle rectangle) + 20 (two triangles) = 170 square centimeters.
Therefore, the correct surface area of the net of the triangular prism is 170 square centimeters. Thank you for your patience.
The surface area of the net of the triangular prism can be found by calculating the area of each individual shape and then summing them up.
1. Top and Bottom Rectangles:
- Area of each rectangle = length * width = 10 * 5 = 50 square centimeters
- Since there are two identical rectangles (top and bottom), the total area for both is 50 * 2 = 100 square centimeters.
2. Middle Rectangle:
- The middle rectangle shares an edge with the base of the triangle, so it has the same dimensions as the top and bottom rectangles.
- Area of the middle rectangle = length * width = 10 * 5 = 50 square centimeters.
3. Two Triangles:
- Area of each triangle = (1/2) * base * height = (1/2) * 5 * 4 = 10 square centimeters
- Since there are two identical triangles, the total area for both is 10 * 2 = 20 square centimeters.
Now, sum up the areas of all the shapes:
Total surface area = 100 (top and bottom rectangles) + 50 (middle rectangle) + 20 (two triangles) = 170 square centimeters.
Therefore, the correct surface area of the net of the triangular prism is 170 square centimeters. Thank you for your patience.
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