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What is the surface area of the triangular prism? 8cm, 10cm, 9cm, 6cm(1 point)
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GPT 3.5
To calculate the surface area of a triangular prism, you need to find the areas of all the surfaces and then sum them up.
The formula for the surface area of a triangular prism is:
Surface Area = 2(Base Area) + (Lateral Area)
where Base Area = 1/2 * base * height of the triangle
Given that the base of the triangle is 8 cm and the height is 6 cm, the Base Area is:
Base Area = 1/2 * 8 * 6 = 24 cm²
Next, we need to find the lateral area of the prism. The lateral area of a triangular prism is equal to the area of the three rectangular faces.
The lateral area of the prism is the sum of the areas of the three rectangles:
Lateral Area = perimeter of the base * height of the prism
Perimeter of the base = 8 + 10 + 9 = 27 cm
Lateral Area = 27 * 6 = 162 cm²
Now we can calculate the total surface area of the triangular prism:
Surface Area = 2(24) + 162 = 48 + 162 = 210 cm²
Therefore, the surface area of the triangular prism with dimensions 8cm, 10cm, 9cm, and 6cm is 210 cm².
The formula for the surface area of a triangular prism is:
Surface Area = 2(Base Area) + (Lateral Area)
where Base Area = 1/2 * base * height of the triangle
Given that the base of the triangle is 8 cm and the height is 6 cm, the Base Area is:
Base Area = 1/2 * 8 * 6 = 24 cm²
Next, we need to find the lateral area of the prism. The lateral area of a triangular prism is equal to the area of the three rectangular faces.
The lateral area of the prism is the sum of the areas of the three rectangles:
Lateral Area = perimeter of the base * height of the prism
Perimeter of the base = 8 + 10 + 9 = 27 cm
Lateral Area = 27 * 6 = 162 cm²
Now we can calculate the total surface area of the triangular prism:
Surface Area = 2(24) + 162 = 48 + 162 = 210 cm²
Therefore, the surface area of the triangular prism with dimensions 8cm, 10cm, 9cm, and 6cm is 210 cm².
Answered by
GPT 3.5
Apologies for the mistake. Let's recalculate the surface area of the triangular prism.
The triangular prism has two triangular faces and three rectangular faces.
1. Triangular faces:
Each triangular face has a base of 8 cm and a height of 6 cm.
Area of one triangular face = 1/2 * base * height = 1/2 * 8 * 6 = 24 cm²
Since there are two triangular faces, their total area is 2 * 24 = 48 cm²
2. Rectangular faces:
The three rectangular faces have dimensions:
- 8 cm x 10 cm (2 faces)
- 10 cm x 9 cm (1 face)
Area of one rectangular face = length x width
Area of two rectangular faces = 2 * (8 * 10) = 160 cm²
Area of one rectangular face = 10 * 9 = 90 cm²
Total area of the rectangular faces = 160 + 90 = 250 cm²
Now, calculate the total surface area by summing up the areas of the triangular and rectangular faces:
Total surface area = 48 (triangular faces) + 250 (rectangular faces) = 298 cm²
Therefore, the surface area of the triangular prism with dimensions 8cm, 10cm, 9cm, and 6cm is 298 cm².
The triangular prism has two triangular faces and three rectangular faces.
1. Triangular faces:
Each triangular face has a base of 8 cm and a height of 6 cm.
Area of one triangular face = 1/2 * base * height = 1/2 * 8 * 6 = 24 cm²
Since there are two triangular faces, their total area is 2 * 24 = 48 cm²
2. Rectangular faces:
The three rectangular faces have dimensions:
- 8 cm x 10 cm (2 faces)
- 10 cm x 9 cm (1 face)
Area of one rectangular face = length x width
Area of two rectangular faces = 2 * (8 * 10) = 160 cm²
Area of one rectangular face = 10 * 9 = 90 cm²
Total area of the rectangular faces = 160 + 90 = 250 cm²
Now, calculate the total surface area by summing up the areas of the triangular and rectangular faces:
Total surface area = 48 (triangular faces) + 250 (rectangular faces) = 298 cm²
Therefore, the surface area of the triangular prism with dimensions 8cm, 10cm, 9cm, and 6cm is 298 cm².
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