Use the image to answer the question.
An illustration shows a two-dimensional net of a triangular prism with all of its sides open and visible. The net appears as three vertical rectangles joined next to each other. All 4 sides of the middle rectangle are drawn with dashed lines. The length of the rectangles is 9 centimeters. The width of the middle rectangle is 5 centimeters. Two right triangles adjoin the middle rectangle at the top and bottom. The perpendicular side measures 12 centimeters and the hypotenuse measures 13 centimeters.
Using the net, what is the surface area of the triangular prism?
(1 point)
___cm2
Surface Area = 2(base area) + (perimeter of base) x height
The base of the triangular prism is a rectangle, so its area is length x width = 9 cm x 5 cm = 45 cm².
The perimeter of the base is 2(9 cm) + 2(5 cm) = 28 cm.
The height of the prism is the same as the perpendicular side of the triangular faces, which is 12 cm.
Now we can calculate the surface area:
2(45 cm²) + (28 cm) x 12 cm = 90 cm² + 336 cm² = 426 cm²
Therefore, the surface area of the triangular prism is 426 cm².
no
I apologize for the error. Let's correct that calculation:
The surface area of a triangular prism can be calculated using the formula: 2(base area) + (perimeter of base) x height.
The base area of the triangular prism is a rectangle with dimensions 9 cm by 5 cm, so the base area is 9 cm * 5 cm = 45 cm².
The perimeter of the base is 2(9 cm) + 2(5 cm) = 18 cm + 10 cm = 28 cm.
The height of the prism is the same as the perpendicular side of the triangular faces, which is 12 cm.
Now we can calculate the surface area:
2(45 cm²) + (28 cm) x 12 cm = 90 cm² + 336 cm² = 426 cm²
Therefore, the surface area of the triangular prism is 426 cm².
Wrong
I apologize for the error. Let's try calculating the surface area of the triangular prism again.
The surface area of a triangular prism can be calculated by adding the area of the two triangular faces and the three rectangular faces.
Area of a rectangle = length x width.
Area of a triangle = 0.5 x base x height.
For the rectangular faces:
2 faces with dimensions 9 cm x 5 cm = 2 * (9 cm * 5 cm) = 90 cm².
For the triangular faces:
2 faces with base 5 cm and height 12 cm = 2 * (0.5 * 5 cm * 12 cm) = 60 cm².
Total surface area of the triangular prism = 90 cm² (for the rectangles) + 60 cm² (for the triangles) = 150 cm².
Therefore, the surface area of the triangular prism is 150 cm².
Use the image to answer the question.
An illustration shows a two-dimensional net of a triangular prism with all of its sides open and visible. The net appears as three vertical rectangles joined next to each other. All 4 sides of the middle rectangle are drawn with dashed lines. The length of the rectangles is 9 centimeters. The width of the middle rectangle is 5 centimeters. Two right triangles adjoin the middle rectangle at the top and bottom. The perpendicular side measures 12 centimeters and the hypotenuse measures 13 centimeters.
Using the net, what is the surface area of the triangular prism?
____cm2
To find the surface area of the triangular prism, we first need to calculate the areas of the individual faces.
1. The middle rectangle:
Area = length x width = 9 cm x 5 cm = 45 cm²
2. The two side rectangles:
Both rectangles have a length of 9 cm and a width of 12 cm (perpendicular side of the triangular face).
Area of each side rectangle = 9 cm x 12 cm = 108 cm²
Combined area of two side rectangles = 2 x 108 cm² = 216 cm²
3. The two triangular faces:
Each triangular face has a base of 5 cm and height of 12 cm.
Area of each triangle = 0.5 x base x height = 0.5 x 5 cm x 12 cm = 30 cm²
Combined area of two triangular faces = 2 x 30 cm² = 60 cm²
Now, calculate the total surface area by adding the areas of all faces:
Total surface area = 45 cm² (middle rectangle) + 216 cm² (side rectangles) + 60 cm² (triangular faces)
Total surface area = 45 cm² + 216 cm² + 60 cm² = 321 cm²
Therefore, the surface area of the triangular prism based on the given net is 321 cm².