To find the surface area of the triangular prism, we first find the surface area of the three rectangles:
1. Top and bottom rectangles:
Surface area = 2 * (length * width) = 2 * (8m * 4m) = 2 * 32m = 64m²
2. Middle rectangle:
Since all sides are open, the surface area is just the area of the rectangle:
Surface area = length * width = 8m * 4m = 32m²
Next, we find the surface area of the two triangles:
Surface area of one triangle = 1/2 * base * height = 1/2 * 8m * 3.4m = 13.6m²
Since there are two triangles, the total surface area for both triangles is 2 * 13.6m² = 27.2m²
Finally, we add up the surface areas of all components:
Total surface area = 64m² (top and bottom rectangles) + 32m² (middle rectangle) + 27.2m² (triangles) = 123.2m²
Therefore, the surface area of the triangular prism is 123.2m².
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 horizontal rectangles joined one on top of the other. All 4 sides of the middle rectangle are drawn with dashed lines. The length of the rectangles is 8 meters. The width of all the rectangles is 4 meters. Two identical triangles adjoin the middle rectangle at the left and right with the perpendicular height of the triangles measuring 3.4 meters.
What is the surface area of the triangular prism whose net is shown below? Round the answer to the nearest hundredth.
(1 point)
___m2
5 answers
no
Let's try again.
To find the total surface area of the triangular prism, we need to calculate the areas of each individual face and then sum them up.
1. The top and bottom faces are rectangles with dimensions 8m (length) by 4m (width). Since there are two of these faces, the total area for the top and bottom faces is:
2 * (8m * 4m) = 64m²
2. The side faces of the triangular prism are the two identical triangles. The area of one triangle is 1/2 * base * height, so the area for both triangles is:
2 * (1/2 * 8m * 3.4m) = 2 * 13.6m² = 27.2m²
3. The middle face (the rectangular face) doesn't contribute to the surface area, as it is open.
Now, we add up the areas of all the faces:
64m² (top and bottom faces) + 27.2m² (side faces) = 91.2m²
Therefore, the surface area of the triangular prism is 91.2m².
To find the total surface area of the triangular prism, we need to calculate the areas of each individual face and then sum them up.
1. The top and bottom faces are rectangles with dimensions 8m (length) by 4m (width). Since there are two of these faces, the total area for the top and bottom faces is:
2 * (8m * 4m) = 64m²
2. The side faces of the triangular prism are the two identical triangles. The area of one triangle is 1/2 * base * height, so the area for both triangles is:
2 * (1/2 * 8m * 3.4m) = 2 * 13.6m² = 27.2m²
3. The middle face (the rectangular face) doesn't contribute to the surface area, as it is open.
Now, we add up the areas of all the faces:
64m² (top and bottom faces) + 27.2m² (side faces) = 91.2m²
Therefore, the surface area of the triangular prism is 91.2m².
nope
Let's try to find the correct answer for the surface area of the triangular prism.
The triangular prism has:
- 2 identical triangular faces.
- 3 rectangular faces.
1. Triangular faces:
Each triangular face has a base of 8m and a height of 3.4m.
The area of one triangle is 1/2 * base * height.
Area of one triangle = 1/2 * 8m * 3.4m = 13.6m².
Since there are 2 identical triangular faces, the total area for both triangles is 2 * 13.6m² = 27.2m².
2. Rectangular faces:
The length of each rectangle is 8m and the width is 4m.
There are 3 rectangles in total.
The area of one rectangle is length * width = 8m * 4m = 32m².
Total area for the 3 rectangular faces is 3 * 32m² = 96m².
Now, we calculate the total surface area by adding the areas of all the faces:
Total surface area = 27.2m² (triangular faces) + 96m² (rectangular faces) = 123.2m².
Therefore, the surface area of the triangular prism is 123.2m².
The triangular prism has:
- 2 identical triangular faces.
- 3 rectangular faces.
1. Triangular faces:
Each triangular face has a base of 8m and a height of 3.4m.
The area of one triangle is 1/2 * base * height.
Area of one triangle = 1/2 * 8m * 3.4m = 13.6m².
Since there are 2 identical triangular faces, the total area for both triangles is 2 * 13.6m² = 27.2m².
2. Rectangular faces:
The length of each rectangle is 8m and the width is 4m.
There are 3 rectangles in total.
The area of one rectangle is length * width = 8m * 4m = 32m².
Total area for the 3 rectangular faces is 3 * 32m² = 96m².
Now, we calculate the total surface area by adding the areas of all the faces:
Total surface area = 27.2m² (triangular faces) + 96m² (rectangular faces) = 123.2m².
Therefore, the surface area of the triangular prism is 123.2m².
1 answer