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
260 square centimeters
260 square centimeters
180 square centimeters
180 square centimeters
280 square centimeters
The surface area of a triangular prism can be calculated by adding the areas of the three rectangular faces and the two triangular faces.
The area of the front triangular face = (1/2) * base * height = (1/2) * 10 * 8 = 40 square centimeters.
The area of the left rectangular face = length * width = 10 * 6 = 60 square centimeters.
The area of the right rectangular face (which is equal in size to the left face) = 60 square centimeters.
The total area of the three rectangular faces = 60 + 60 = 120 square centimeters.
The area of the top triangular face = 40 square centimeters.
The area of the bottom triangular face is also equal in size to the top face, which is 40 square centimeters.
The total surface area of the triangular prism = 120 + 40 + 40 = 200 square centimeters.
Therefore, the surface area of the triangular prism is 200 square centimeters.
200 isnt an option
I apologize for the mistake in my calculation. Let me re-calculate the surface area of the triangular prism based on the provided dimensions:
Area of the front triangular face = (1/2) * base * height = (1/2) * 10 * 8 = 40 square centimeters
Area of the left rectangular face = length * width = 10 * 6 = 60 square centimeters
Area of the right rectangular face = 60 square centimeters
Total area of the two rectangular faces = 60 + 60 = 120 square centimeters
Area of the top triangular face = 40 square centimeters
Area of the bottom triangular face = 40 square centimeters
Therefore, the total surface area of the triangular prism is 120 (rectangular faces) + 40 + 40 (triangular faces) = 200 square centimeters.
So, the correct surface area of the triangular prism is 200 square centimeters.
280 square centimeters
280 square centimeters
260 square centimeters
260 square centimeters
320 square centimeters
320 square centimeters
180 square centimeters
are the options
I apologize for the mistakes in my initial responses. Let me reconsider the calculation of the surface area of the triangular prism based on the provided dimensions.
Area of the front triangular face = (1/2) * base * height = (1/2) * 10 * 8 = 40 square centimeters
Area of the left rectangular face = length * width = 10 * 6 = 60 square centimeters
Area of the right rectangular face = 60 square centimeters (since both rectangles are equal in size)
Area of the top triangular face = 40 square centimeters
Area of the bottom triangular face = 40 square centimeters
Total area of the three rectangular faces = 60 (left) + 60 (right) = 120 square centimeters
Total surface area of the triangular prism = 120 (rectangular faces) + 40 + 40 (triangular faces) = 200 square centimeters
Therefore, the correct surface area of the triangular prism is 200 square centimeters.