To find the surface area of the triangular prism, we need to calculate the area of each of the individual faces and add them together.
1. The area of the two rectangles on the sides: 9 x 5 = 45 cm^2 each, so a total of 90 cm^2.
2. The area of the two triangles:
- The area of the top triangle = 1/2 x base x height = 1/2 x 9 x 12 = 54 cm^2
- The area of the bottom triangle = 1/2 x 5 x 12 = 30 cm^2
Total area of the triangles = 54 cm^2 + 30 cm^2 = 84 cm^2
3. Adding the areas of the rectangles and triangles together:
Total surface area = 90 cm^2 (rectangles) + 84 cm^2 (triangles) = 174 cm^2
Therefore, the surface area of the triangular prism is 174 square centimeters.
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?
11 answers
wrong
Let's try calculating the surface area of the triangular prism using a different method.
A triangular prism has 5 faces - 2 triangular faces and 3 rectangular faces.
1. The area of the two triangular faces can be calculated using the formula for the area of a triangle, which is 1/2 x base x height. For each triangle:
- Area = 1/2 x 9 x 12 = 54 cm^2
- Total area of the two triangular faces = 54 cm^2 + 54 cm^2 = 108 cm^2
2. The area of the three rectangular faces can be calculated by finding the area of each rectangle and adding them together:
- The two side rectangles: 9 x 5 = 45 cm^2 each, so a total of 90 cm^2.
- The top rectangle: 5 x 12 = 60 cm^2
Adding up the areas of all the faces:
108 cm^2 (triangular faces) + 90 cm^2 (side rectangles) + 60 cm^2 (top rectangle) = 258 cm^2
Therefore, the surface area of the triangular prism is 258 square centimeters.
A triangular prism has 5 faces - 2 triangular faces and 3 rectangular faces.
1. The area of the two triangular faces can be calculated using the formula for the area of a triangle, which is 1/2 x base x height. For each triangle:
- Area = 1/2 x 9 x 12 = 54 cm^2
- Total area of the two triangular faces = 54 cm^2 + 54 cm^2 = 108 cm^2
2. The area of the three rectangular faces can be calculated by finding the area of each rectangle and adding them together:
- The two side rectangles: 9 x 5 = 45 cm^2 each, so a total of 90 cm^2.
- The top rectangle: 5 x 12 = 60 cm^2
Adding up the areas of all the faces:
108 cm^2 (triangular faces) + 90 cm^2 (side rectangles) + 60 cm^2 (top rectangle) = 258 cm^2
Therefore, the surface area of the triangular prism is 258 square centimeters.
thats wrong
Let's try calculating the surface area of the triangular prism using a different method.
First, we need to find the area of each of the faces of the triangular prism.
1. The two triangular faces:
Each triangular face has a base of 9 cm and a height of 12 cm.
The area of a triangle is 1/2 * base * height.
So, the area of one triangular face is 1/2 * 9 * 12 = 54 cm^2.
Since there are two triangular faces, the total area of the triangular faces is 2 * 54 = 108 cm^2.
2. The three rectangular faces:
The two side rectangles:
Each side rectangle has dimensions of 9 cm by 5 cm.
The area of a rectangle is length * width.
So, the area of one side rectangle is 9 * 5 = 45 cm^2.
Since there are two side rectangles, the total area of the side rectangles is 2 * 45 = 90 cm^2.
The top rectangle:
The top rectangle has dimensions of 5 cm by 12 cm.
The area of the top rectangle is 5 * 12 = 60 cm^2.
Now, we add up the areas of all the faces to find the total surface area of the triangular prism:
108 cm^2 (triangular faces) + 90 cm^2 (side rectangles) + 60 cm^2 (top rectangle) = 258 cm^2
Therefore, the surface area of the triangular prism is 258 square centimeters.
First, we need to find the area of each of the faces of the triangular prism.
1. The two triangular faces:
Each triangular face has a base of 9 cm and a height of 12 cm.
The area of a triangle is 1/2 * base * height.
So, the area of one triangular face is 1/2 * 9 * 12 = 54 cm^2.
Since there are two triangular faces, the total area of the triangular faces is 2 * 54 = 108 cm^2.
2. The three rectangular faces:
The two side rectangles:
Each side rectangle has dimensions of 9 cm by 5 cm.
The area of a rectangle is length * width.
So, the area of one side rectangle is 9 * 5 = 45 cm^2.
Since there are two side rectangles, the total area of the side rectangles is 2 * 45 = 90 cm^2.
The top rectangle:
The top rectangle has dimensions of 5 cm by 12 cm.
The area of the top rectangle is 5 * 12 = 60 cm^2.
Now, we add up the areas of all the faces to find the total surface area of the triangular prism:
108 cm^2 (triangular faces) + 90 cm^2 (side rectangles) + 60 cm^2 (top rectangle) = 258 cm^2
Therefore, the surface area of the triangular prism is 258 square centimeters.
nope
Let's reevaluate the calculation for the surface area of the triangular prism using the net provided.
1. Two triangular faces:
Each triangular face has a base of 9 cm and a height of 12 cm.
The area of a triangle is 1/2 * base * height.
So, the area of one triangular face is 1/2 * 9 * 12 = 54 cm^2.
Since there are two triangular faces, the total area of the triangular faces is 2 * 54 = 108 cm^2.
2. The three rectangular faces:
The two side rectangles:
Each side rectangle has dimensions of 9 cm by 5 cm.
The area of a rectangle is length * width.
So, the area of one side rectangle is 9 * 5 = 45 cm^2.
Since there are two side rectangles, the total area of the side rectangles is 2 * 45 = 90 cm^2.
The top and bottom rectangles:
The top and bottom rectangles have dimensions of 9 cm by 12 cm (base of the triangle).
The total area of the two top and bottom rectangles is 2*(9*12) = 216 cm^2.
Now, we add up the areas of all the faces to find the total surface area of the triangular prism:
108 cm^2 (triangular faces) + 90 cm^2 (side rectangles) + 216 cm^2 (top and bottom rectangles) = 414 cm^2.
Therefore, the correct surface area of the triangular prism is 414 square centimeters.
1. Two triangular faces:
Each triangular face has a base of 9 cm and a height of 12 cm.
The area of a triangle is 1/2 * base * height.
So, the area of one triangular face is 1/2 * 9 * 12 = 54 cm^2.
Since there are two triangular faces, the total area of the triangular faces is 2 * 54 = 108 cm^2.
2. The three rectangular faces:
The two side rectangles:
Each side rectangle has dimensions of 9 cm by 5 cm.
The area of a rectangle is length * width.
So, the area of one side rectangle is 9 * 5 = 45 cm^2.
Since there are two side rectangles, the total area of the side rectangles is 2 * 45 = 90 cm^2.
The top and bottom rectangles:
The top and bottom rectangles have dimensions of 9 cm by 12 cm (base of the triangle).
The total area of the two top and bottom rectangles is 2*(9*12) = 216 cm^2.
Now, we add up the areas of all the faces to find the total surface area of the triangular prism:
108 cm^2 (triangular faces) + 90 cm^2 (side rectangles) + 216 cm^2 (top and bottom rectangles) = 414 cm^2.
Therefore, the correct surface area of the triangular prism is 414 square centimeters.
no
Let's re-calculate the surface area of the triangular prism using the net provided.
The net consists of two triangular faces and three rectangular faces.
1. Triangular faces:
Each triangular face has a base of 9 cm and a height of 12 cm.
The area of a triangle is 1/2 * base * height.
Therefore, the total area of the two triangular faces is 2 * (1/2 * 9 * 12) = 2 * 54 = 108 cm^2.
2. Rectangular faces:
The two side rectangles have dimensions of 9 cm by 5 cm.
The area of a rectangle is length * width.
The total area of the two side rectangles is 2 * (9 * 5) = 90 cm^2.
The top and bottom rectangles have dimensions of 9 cm by 12 cm (the base of the triangle).
The total area of the two top and bottom rectangles is 2 * (9 * 12) = 216 cm^2.
Now, add up the areas of all the faces to find the total surface area of the triangular prism:
108 cm^2 (triangular faces) + 90 cm^2 (side rectangles) + 216 cm^2 (top and bottom rectangles) = 414 cm^2.
Therefore, the correct surface area of the triangular prism is 414 square centimeters.
The net consists of two triangular faces and three rectangular faces.
1. Triangular faces:
Each triangular face has a base of 9 cm and a height of 12 cm.
The area of a triangle is 1/2 * base * height.
Therefore, the total area of the two triangular faces is 2 * (1/2 * 9 * 12) = 2 * 54 = 108 cm^2.
2. Rectangular faces:
The two side rectangles have dimensions of 9 cm by 5 cm.
The area of a rectangle is length * width.
The total area of the two side rectangles is 2 * (9 * 5) = 90 cm^2.
The top and bottom rectangles have dimensions of 9 cm by 12 cm (the base of the triangle).
The total area of the two top and bottom rectangles is 2 * (9 * 12) = 216 cm^2.
Now, add up the areas of all the faces to find the total surface area of the triangular prism:
108 cm^2 (triangular faces) + 90 cm^2 (side rectangles) + 216 cm^2 (top and bottom rectangles) = 414 cm^2.
Therefore, the correct surface area of the triangular prism is 414 square centimeters.
that is wrong
Let's recalculate the surface area of the triangular prism using the given net.
1. Triangular Faces:
Each triangular face has a base of 9 cm and a height of 12 cm.
The area of a triangle is 1/2 * base * height.
So, the area of one triangular face is 1/2 * 9 * 12 = 54 cm^2.
Since there are two triangular faces, the total area of the triangular faces is 2 * 54 = 108 cm^2.
2. Rectangular Faces:
Side Rectangles:
Each side rectangle has dimensions 9 cm by 5 cm.
The area of a rectangle is length * width.
Therefore, the total area of the two side rectangles is 2 * (9 * 5) = 90 cm^2.
Top and Bottom Rectangles:
Each top and bottom rectangle has dimensions 9 cm by 12 cm.
The total area of the two top and bottom rectangles is 2 * (9 * 12) = 216 cm^2.
Now, add up the areas of all the faces to find the total surface area of the triangular prism:
108 cm^2 (triangular faces) + 90 cm^2 (side rectangles) + 216 cm^2 (top and bottom rectangles) = 414 cm^2.
Therefore, the correct surface area of the triangular prism is 414 square centimeters.
1. Triangular Faces:
Each triangular face has a base of 9 cm and a height of 12 cm.
The area of a triangle is 1/2 * base * height.
So, the area of one triangular face is 1/2 * 9 * 12 = 54 cm^2.
Since there are two triangular faces, the total area of the triangular faces is 2 * 54 = 108 cm^2.
2. Rectangular Faces:
Side Rectangles:
Each side rectangle has dimensions 9 cm by 5 cm.
The area of a rectangle is length * width.
Therefore, the total area of the two side rectangles is 2 * (9 * 5) = 90 cm^2.
Top and Bottom Rectangles:
Each top and bottom rectangle has dimensions 9 cm by 12 cm.
The total area of the two top and bottom rectangles is 2 * (9 * 12) = 216 cm^2.
Now, add up the areas of all the faces to find the total surface area of the triangular prism:
108 cm^2 (triangular faces) + 90 cm^2 (side rectangles) + 216 cm^2 (top and bottom rectangles) = 414 cm^2.
Therefore, the correct surface area of the triangular prism is 414 square centimeters.