Use the image to answer the question.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 centimetersSkip to navigation
To find the surface area of the triangular prism, we need to find the areas of each of the individual faces and then add them together.
First, let's find the area of the front triangular face:
Area = 1/2 * base * height
Area = 1/2 * 6 * 8
Area = 24 square centimeters
Next, let's find the area of the right rectangular face:
Area = length * width
Area = 10 * 9
Area = 90 square centimeters
Since there are two triangular faces and three rectangular faces on a triangular prism, we need to find the areas of the other triangular face and two rectangular faces.
Another triangular face: 24 square centimeters
Two other rectangular faces: 90 and 9
Total Area: 24 + 90 + 24 + 90 + 9
Total area = 237 square centimeters
Therefore, the surface area of the triangular prism is 237 square centimeters.
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To find the surface area of a triangular prism, we need to find the areas of all the individual faces and then add them together.
1. Front triangular face:
Area = 1/2 * base * height
Area = 1/2 * 6 * 8
Area = 24 square centimeters
2. Back triangular face (since the front and back triangular faces are congruent):
Area = 24 square centimeters
3. Rectangular sides:
Area = length * width
Area = 10 * 9
Area = 90 square centimeters (for each side)
4. Top rectangular face:
Area = base * height
Area = 6 * 10
Area = 60 square centimeters
Now, add up the areas of all the faces:
24 (front triangle) + 24 (back triangle) + 90 (rectangular side) + 90 (rectangular side) + 60 (top rectangle)
Total surface area = 288 square centimeters
Therefore, the correct surface area of the triangular prism is 288 square centimeters.
Surface Area of Triangular Prisms Practice
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Question
Use the image to answer the question.
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?
To find the surface area of the net of the triangular prism, we need to find the areas of all the individual faces and then add them together.
1. Top rectangle:
Area = length * width
Area = 10 * 5
Area = 50 square centimeters
2. Bottom rectangle:
Area = 10 * 5
Area = 50 square centimeters
3. Middle rectangle:
Area = 10 * 4
Area = 40 square centimeters
4. Left triangle:
Area = 1/2 * base * height
Area = 1/2 * 5 * 4
Area = 10 square centimeters
5. Right triangle (since they are identical):
Area = 10 square centimeters
Now, add up the areas of all the faces:
50 (top rectangle) + 50 (bottom rectangle) + 40 (middle rectangle) + 10 (left triangle) + 10 (right triangle)
Total surface area = 160 square centimeters
Therefore, the surface area of the net of the triangular prism is 160 square centimeters.