Question
Solve for the surface area of the triangular prism.
(1 point)
(1 point)
Answers
Answer
Surface Area of Triangular Prisms Quick Check
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Question
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
320 square centimeters
320 square centimeters
180 square centimeters
180 square centimeters
280 square centimeters
280 square centimeters
260 square centimeters
Answer
Solve for the surface area of the triangular prism.
(1 point)
Responses
320 square centimeters
320 square centimeters
180 square centimeters
180 square centimeters
280 square centimeters
280 square centimeters
260 square centimeters
(1 point)
Responses
320 square centimeters
320 square centimeters
180 square centimeters
180 square centimeters
280 square centimeters
280 square centimeters
260 square centimeters
Answered by
GPT 3.5
To calculate the surface area of a triangular prism, you need to find the areas of the three rectangular faces and the two triangular faces and then add them together.
Let's denote the dimensions of the triangular prism as follows:
- Base of the triangle = b
- Height of the triangle = h
- Base of the prism = b
- Height of the prism (distance between the two triangular bases) = h
- Length of the prism = l
The formula for the surface area of a triangular prism is:
Surface Area = 2 * Area of base triangle + Perimeter of base triangle * Height of the prism + 2 * Area of each rectangular face
1. Area of the base triangle:
Area = (1/2) * base * height
Area = (1/2) * b * h
2. Perimeter of the base triangle:
Perimeter = a + b + c
3. Area of each rectangular face:
Area = length * height
Area = l * h
Now calculate the surface area of the triangular prism using the above formulas:
Surface Area = 2 * (1/2 * b * h) + (a+b+c) * h + 2 * (l * h)
Surface Area = b * h + (a + b + c) * h + 2 * l * h
Surface Area = b * h + h * (a + b + c) + 2 * l * h
Just input the numerical values of b, h, a, c, and l to calculate the surface area of the given triangular prism.
Let's denote the dimensions of the triangular prism as follows:
- Base of the triangle = b
- Height of the triangle = h
- Base of the prism = b
- Height of the prism (distance between the two triangular bases) = h
- Length of the prism = l
The formula for the surface area of a triangular prism is:
Surface Area = 2 * Area of base triangle + Perimeter of base triangle * Height of the prism + 2 * Area of each rectangular face
1. Area of the base triangle:
Area = (1/2) * base * height
Area = (1/2) * b * h
2. Perimeter of the base triangle:
Perimeter = a + b + c
3. Area of each rectangular face:
Area = length * height
Area = l * h
Now calculate the surface area of the triangular prism using the above formulas:
Surface Area = 2 * (1/2 * b * h) + (a+b+c) * h + 2 * (l * h)
Surface Area = b * h + (a + b + c) * h + 2 * l * h
Surface Area = b * h + h * (a + b + c) + 2 * l * h
Just input the numerical values of b, h, a, c, and l to calculate the surface area of the given triangular prism.
Answered by
GPT 3.5
To solve for the surface area of the triangular prism, you need to calculate the areas of the faces and then add them up.
Given:
Base of the triangle (b) = 10 cm
Height of the triangle (h) = 8 cm
Base of the prism (b) = 10 cm
Height of the prism (h) = 8 cm
Width of the rectangular face (w) = 6 cm
1. Area of the base triangle:
Area = (1/2) * base * height
Area = (1/2) * 10 cm * 8 cm
Area = 40 square cm
2. Perimeter of the base triangle:
Since all sides of the triangle measure 10 cm, the perimeter is 10 + 10 + 10 = 30 cm
3. Area of each rectangular face:
Area = length * width
Area = 8 cm * 6 cm
Area = 48 square cm
Now calculate the surface area of the triangular prism:
Surface Area = 2 * (Area of base triangle) + (Perimeter of base triangle) * Height of the prism + 2 * (Area of each rectangular face)
Surface Area = 2 * 40 square cm + 30 cm * 8 cm + 2 * 48 square cm
Surface Area = 80 square cm + 240 square cm + 96 square cm
Surface Area = 416 square cm
Therefore, the surface area of the triangular prism is 416 square centimeters.
Given:
Base of the triangle (b) = 10 cm
Height of the triangle (h) = 8 cm
Base of the prism (b) = 10 cm
Height of the prism (h) = 8 cm
Width of the rectangular face (w) = 6 cm
1. Area of the base triangle:
Area = (1/2) * base * height
Area = (1/2) * 10 cm * 8 cm
Area = 40 square cm
2. Perimeter of the base triangle:
Since all sides of the triangle measure 10 cm, the perimeter is 10 + 10 + 10 = 30 cm
3. Area of each rectangular face:
Area = length * width
Area = 8 cm * 6 cm
Area = 48 square cm
Now calculate the surface area of the triangular prism:
Surface Area = 2 * (Area of base triangle) + (Perimeter of base triangle) * Height of the prism + 2 * (Area of each rectangular face)
Surface Area = 2 * 40 square cm + 30 cm * 8 cm + 2 * 48 square cm
Surface Area = 80 square cm + 240 square cm + 96 square cm
Surface Area = 416 square cm
Therefore, the surface area of the triangular prism is 416 square centimeters.
Answered by
GPT 3.5
To find the surface area of the triangular prism, we need to calculate the areas of the different faces and then add them together.
Given:
- Base of the triangle (b) = 10 cm
- Height of the triangle (h) = 8 cm
- Base of the prism (b) = 10 cm
- Height of the prism (h) = 8 cm
- Width of the rectangular face (w) = 6 cm
1. Area of the base triangle:
Area = (1/2) * base * height
Area = (1/2) * 10 cm * 8 cm
Area = 40 square cm
2. Perimeter of the base triangle:
Since all sides of the triangle measure 10 cm, the perimeter is 10 + 10 + 10 = 30 cm
3. Area of each rectangular face:
Area = length * width
Area = 8 cm * 6 cm
Area = 48 square cm
Now calculate the surface area of the triangular prism:
Surface Area = 2 * (Area of base triangle) + Perimeter of base triangle * Height of the prism + 2 * (Area of each rectangular face)
Surface Area = 2 * 40 square cm + 30 cm * 8 cm + 2 * 48 square cm
Surface Area = 80 square cm + 240 square cm + 96 square cm
Surface Area = 416 square cm
Therefore, the correct answer is not provided in the options given. The surface area of the triangular prism is 416 square centimeters.
Given:
- Base of the triangle (b) = 10 cm
- Height of the triangle (h) = 8 cm
- Base of the prism (b) = 10 cm
- Height of the prism (h) = 8 cm
- Width of the rectangular face (w) = 6 cm
1. Area of the base triangle:
Area = (1/2) * base * height
Area = (1/2) * 10 cm * 8 cm
Area = 40 square cm
2. Perimeter of the base triangle:
Since all sides of the triangle measure 10 cm, the perimeter is 10 + 10 + 10 = 30 cm
3. Area of each rectangular face:
Area = length * width
Area = 8 cm * 6 cm
Area = 48 square cm
Now calculate the surface area of the triangular prism:
Surface Area = 2 * (Area of base triangle) + Perimeter of base triangle * Height of the prism + 2 * (Area of each rectangular face)
Surface Area = 2 * 40 square cm + 30 cm * 8 cm + 2 * 48 square cm
Surface Area = 80 square cm + 240 square cm + 96 square cm
Surface Area = 416 square cm
Therefore, the correct answer is not provided in the options given. The surface area of the triangular prism is 416 square centimeters.