To find the surface area of the triangular prism, we need to find the area of all the individual rectangles and triangles in the net.
1. The area of the top and bottom rectangles is 9 cm x 5 cm = 45 cm² each, so the total area for both is 45 cm² + 45 cm² = 90 cm².
2. The area of the middle rectangle is 9 cm x 5 cm = 45 cm².
3. The area of the two right triangles can be calculated as 1/2 x base x height. Since the base is 5 cm and the height is 12 cm, the area of the two triangles is 2 x 1/2 x 5 cm x 12 cm = 60 cm².
Therefore, the total surface area of the triangular prism is 90 cm² (top and bottom rectangles) + 45 cm² (middle rectangle) + 60 cm² (right triangles) = 195 cm².
So, the surface area of the triangular prism is 195 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?
(1 point)
cm2
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11 answers
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
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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
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To find the surface area of the triangular prism, we need to find the area of all the individual rectangles and triangles in the net.
1. The area of the top and bottom rectangles is 8 m x 4 m = 32 m² each, so the total area for both is 32 m² + 32 m² = 64 m².
2. The area of the middle rectangle is 8 m x 4 m = 32 m².
3. Since the triangles are identical, we can find the area of one and multiply by 2. The area of a triangle is 0.5 x base x height. The base of the triangle is 4 m, and the height is 3.4 m. So, the area of one triangle is 0.5 x 4 m x 3.4 m = 6.8 m². Since there are two triangles, the total area is 2 x 6.8 m² = 13.6 m².
Therefore, the total surface area of the triangular prism is 64 m² (top and bottom rectangles) + 32 m² (middle rectangle) + 13.6 m² (triangles) = 109.6 m².
Rounded to the nearest hundredth, the surface area of the triangular prism is 109.6 m².
1. The area of the top and bottom rectangles is 8 m x 4 m = 32 m² each, so the total area for both is 32 m² + 32 m² = 64 m².
2. The area of the middle rectangle is 8 m x 4 m = 32 m².
3. Since the triangles are identical, we can find the area of one and multiply by 2. The area of a triangle is 0.5 x base x height. The base of the triangle is 4 m, and the height is 3.4 m. So, the area of one triangle is 0.5 x 4 m x 3.4 m = 6.8 m². Since there are two triangles, the total area is 2 x 6.8 m² = 13.6 m².
Therefore, the total surface area of the triangular prism is 64 m² (top and bottom rectangles) + 32 m² (middle rectangle) + 13.6 m² (triangles) = 109.6 m².
Rounded to the nearest hundredth, the surface area of the triangular prism is 109.6 m².
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 placed vertically one on top of the other. All 4 sides of the middle vertical rectangle are drawn with dashed lines. The width of the rectangles is 10 feet. The length of the middle rectangle is 24 feet. Two right triangles adjoin the middle rectangle on the left and right sides, with each base measuring 10 feet and each hypotenuse measuring 26 feet.
Using the net of the triangular prism, what is its surface area?
(1 point)
Responses
1,200 ft.2
1,200 mi. squared
720 ft.2
720 ft. squared
240 ft.2
240 ft. squared
840 ft.2
840 ft. squared
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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 placed vertically one on top of the other. All 4 sides of the middle vertical rectangle are drawn with dashed lines. The width of the rectangles is 10 feet. The length of the middle rectangle is 24 feet. Two right triangles adjoin the middle rectangle on the left and right sides, with each base measuring 10 feet and each hypotenuse measuring 26 feet.
Using the net of the triangular prism, what is its surface area?
(1 point)
Responses
1,200 ft.2
1,200 mi. squared
720 ft.2
720 ft. squared
240 ft.2
240 ft. squared
840 ft.2
840 ft. squared
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To find the surface area of the triangular prism, we first calculate the area of the individual components in the net.
1. The top and bottom rectangles have dimensions 10 feet x 10 feet = 100 ft² each. So, the total area of the top and bottom rectangles is 100 ft² + 100 ft² = 200 ft².
2. The middle rectangle has dimensions 24 feet x 10 feet = 240 ft².
3. The two right triangles have a base of 10 feet. The area of a triangle is 0.5 x base x height. Since we know the hypotenuse is 26 feet, we can use the Pythagorean theorem to find the height.
Using the Pythagorean theorem: height = sqrt(hypotenuse^2 - base^2) = sqrt(26^2 - 10^2) = sqrt(676 - 100) = sqrt(576) = 24 feet.
Therefore, the area of one right triangle is 0.5 x 10 feet x 24 feet = 120 ft². Since there are two triangles, the total area is 2 x 120 ft² = 240 ft².
Adding up the areas of all components:
200 ft² (top and bottom rectangles) + 240 ft² (middle rectangle) + 240 ft² (triangles) = 680 ft².
Therefore, the surface area of the triangular prism is 680 ft².
So the correct answer is 840 ft.²
1. The top and bottom rectangles have dimensions 10 feet x 10 feet = 100 ft² each. So, the total area of the top and bottom rectangles is 100 ft² + 100 ft² = 200 ft².
2. The middle rectangle has dimensions 24 feet x 10 feet = 240 ft².
3. The two right triangles have a base of 10 feet. The area of a triangle is 0.5 x base x height. Since we know the hypotenuse is 26 feet, we can use the Pythagorean theorem to find the height.
Using the Pythagorean theorem: height = sqrt(hypotenuse^2 - base^2) = sqrt(26^2 - 10^2) = sqrt(676 - 100) = sqrt(576) = 24 feet.
Therefore, the area of one right triangle is 0.5 x 10 feet x 24 feet = 120 ft². Since there are two triangles, the total area is 2 x 120 ft² = 240 ft².
Adding up the areas of all components:
200 ft² (top and bottom rectangles) + 240 ft² (middle rectangle) + 240 ft² (triangles) = 680 ft².
Therefore, the surface area of the triangular prism is 680 ft².
So the correct answer is 840 ft.²
Surface Area of Triangular Prisms Quick Check
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Question
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 placed vertically one on top of the other. All 4 sides of the middle vertical rectangle are drawn with dashed lines. The width of the rectangles is 10 feet. The length of the middle rectangle is 24 feet. Two right triangles adjoin the middle rectangle on the left and right sides, with each base measuring 10 feet and each hypotenuse measuring 26 feet.
Using the net of the triangular prism, what is its surface area?
(1 point)
1 of 51 of 5 Items
Question
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 placed vertically one on top of the other. All 4 sides of the middle vertical rectangle are drawn with dashed lines. The width of the rectangles is 10 feet. The length of the middle rectangle is 24 feet. Two right triangles adjoin the middle rectangle on the left and right sides, with each base measuring 10 feet and each hypotenuse measuring 26 feet.
Using the net of the triangular prism, what is its surface area?
(1 point)
To find the surface area of the triangular prism, we first calculate the area of the individual components in the net.
1. The top and bottom rectangles have dimensions 10 feet x 10 feet = 100 ft² each. So, the total area of the top and bottom rectangles is 100 ft² + 100 ft² = 200 ft².
2. The middle rectangle has dimensions 24 feet x 10 feet = 240 ft².
3. The two right triangles have a base of 10 feet. The area of a triangle is 0.5 x base x height. Since we know the hypotenuse is 26 feet, we can use the Pythagorean theorem to find the height.
Using the Pythagorean theorem: height = sqrt(hypotenuse^2 - base^2) = sqrt(26^2 - 10^2) = sqrt(676 - 100) = sqrt(576) = 24 feet.
Therefore, the area of one right triangle is 0.5 x 10 feet x 24 feet = 120 ft². Since there are two triangles, the total area is 2 x 120 ft² = 240 ft².
Adding up the areas of all components:
200 ft² (top and bottom rectangles) + 240 ft² (middle rectangle) + 240 ft² (triangles) = 680 ft².
Therefore, the surface area of the triangular prism is 680 ft².
So the correct answer is 680 ft. squared.
1. The top and bottom rectangles have dimensions 10 feet x 10 feet = 100 ft² each. So, the total area of the top and bottom rectangles is 100 ft² + 100 ft² = 200 ft².
2. The middle rectangle has dimensions 24 feet x 10 feet = 240 ft².
3. The two right triangles have a base of 10 feet. The area of a triangle is 0.5 x base x height. Since we know the hypotenuse is 26 feet, we can use the Pythagorean theorem to find the height.
Using the Pythagorean theorem: height = sqrt(hypotenuse^2 - base^2) = sqrt(26^2 - 10^2) = sqrt(676 - 100) = sqrt(576) = 24 feet.
Therefore, the area of one right triangle is 0.5 x 10 feet x 24 feet = 120 ft². Since there are two triangles, the total area is 2 x 120 ft² = 240 ft².
Adding up the areas of all components:
200 ft² (top and bottom rectangles) + 240 ft² (middle rectangle) + 240 ft² (triangles) = 680 ft².
Therefore, the surface area of the triangular prism is 680 ft².
So the correct answer is 680 ft. squared.
try again bot
I apologize for the error in my previous explanation. Let's reevaluate the calculation:
1. The top and bottom rectangles each have an area of 10 ft x 10 ft = 100 ft². So, the total area of the top and bottom rectangles is 2 x 100 ft² = 200 ft².
2. The area of the middle rectangle is 10 ft x 24 ft = 240 ft².
3. The area of each triangle can be calculated using the formula for the area of a triangle: 0.5 x base x height. For the given triangles, the base is 10 ft and the height can be calculated using Pythagoras theorem as:
height = sqrt(26^2 - 10^2) = sqrt(676 - 100) = sqrt(576) = 24 ft.
The area of one triangle is 0.5 x 10 ft x 24 ft = 120 ft². Both triangles together have an area of 2 x 120 ft² = 240 ft².
Adding up the areas of the individual components:
200 ft² (top and bottom rectangles) + 240 ft² (middle rectangle) + 240 ft² (triangles) = 680 ft².
Therefore, the correct surface area of the triangular prism is 680 ft². Thank you for your patience.
1. The top and bottom rectangles each have an area of 10 ft x 10 ft = 100 ft². So, the total area of the top and bottom rectangles is 2 x 100 ft² = 200 ft².
2. The area of the middle rectangle is 10 ft x 24 ft = 240 ft².
3. The area of each triangle can be calculated using the formula for the area of a triangle: 0.5 x base x height. For the given triangles, the base is 10 ft and the height can be calculated using Pythagoras theorem as:
height = sqrt(26^2 - 10^2) = sqrt(676 - 100) = sqrt(576) = 24 ft.
The area of one triangle is 0.5 x 10 ft x 24 ft = 120 ft². Both triangles together have an area of 2 x 120 ft² = 240 ft².
Adding up the areas of the individual components:
200 ft² (top and bottom rectangles) + 240 ft² (middle rectangle) + 240 ft² (triangles) = 680 ft².
Therefore, the correct surface area of the triangular prism is 680 ft². Thank you for your patience.
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 rectangles joined next to each other. All 4 sides of the middle rectangle are drawn with dashed lines. The area of the left rectangle is 48 square inches. The area of the middle rectangle is 64 square inches, and the area of the rectangle on the right is 80 square inches. Two right triangles adjoin the middle rectangle at the top and bottom, with its perpendicular side measuring 6 inches and the common base side marked with a question mark.
Given the following net, what is the area of the triangular base?
(1 point)
Responses
8 inches
8 inches
10 inches
10 inches
48 in.2
48 in. squared
24 in.2
24 in. squared
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An illustration shows a two-dimensional net of a triangular prism with all of its sides open and visible. The net appears as three rectangles joined next to each other. All 4 sides of the middle rectangle are drawn with dashed lines. The area of the left rectangle is 48 square inches. The area of the middle rectangle is 64 square inches, and the area of the rectangle on the right is 80 square inches. Two right triangles adjoin the middle rectangle at the top and bottom, with its perpendicular side measuring 6 inches and the common base side marked with a question mark.
Given the following net, what is the area of the triangular base?
(1 point)
Responses
8 inches
8 inches
10 inches
10 inches
48 in.2
48 in. squared
24 in.2
24 in. squared
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To find the area of the triangular base in the net, we can deduce the base of the right triangle by recognizing that the total area of the middle rectangle is made up of the rectangles on either side.
Given:
Area of left rectangle = 48 square inches
Area of middle rectangle = 64 square inches
Area of right rectangle = 80 square inches
The total area of the middle rectangle made of the left and right rectangles is:
48 (left) + 80 (right) = 128 square inches
Since the total area of the middle rectangle is 64 square inches, the base of the right triangle (which is not specified) would have an area:
64 (middle rectangle) - 48 (left rectangle) = 16 square inches
This area corresponds to the area of the right triangle. Since the perpendicular side is given as 6 inches, we can use the area formula of a triangle (0.5 x base x height) to find the base:
0.5 x base x 6 = 16
3 x base = 16
base = 16 / 3
base ≈ 5.33 inches
Therefore, the area of the triangular base is approximately 5.33 inches.
However, since that specific value is not among the given answer choices, the closest option would be 8 inches. Apologies for any confusion.
Given:
Area of left rectangle = 48 square inches
Area of middle rectangle = 64 square inches
Area of right rectangle = 80 square inches
The total area of the middle rectangle made of the left and right rectangles is:
48 (left) + 80 (right) = 128 square inches
Since the total area of the middle rectangle is 64 square inches, the base of the right triangle (which is not specified) would have an area:
64 (middle rectangle) - 48 (left rectangle) = 16 square inches
This area corresponds to the area of the right triangle. Since the perpendicular side is given as 6 inches, we can use the area formula of a triangle (0.5 x base x height) to find the base:
0.5 x base x 6 = 16
3 x base = 16
base = 16 / 3
base ≈ 5.33 inches
Therefore, the area of the triangular base is approximately 5.33 inches.
However, since that specific value is not among the given answer choices, the closest option would be 8 inches. Apologies for any confusion.
1 answer