Which of the following describes a valid method for calculating the surface area of a triangular prism?(1 point)
Responses
Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of all five shapes.
Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of all five shapes.
Decompose the triangular prism into three triangles and two rectangles. Find the sum of three times the area of one triangle and twice the area of one rectangle.
Decompose the triangular prism into three triangles and two rectangles. Find the sum of three times the area of one triangle and twice the area of one rectangle.
Decompose the triangular prism into three triangles and two rectangles. Find the sum of the area of all five shapes.
Decompose the triangular prism into three triangles and two rectangles. Find the sum of the area of all five shapes.
Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of one triangle and three times the area of one rectangle.
9 answers
Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of all five shapes.
Use the image to answer the question.
An illustration shows a triangular prism. The front triangular face is visible. The left rectangular face is visible. The sides and edges that are not visible are indicated by dashed lines. Parts are labeled with measurements. All sides of the triangle measure 10 centimeters. The perpendicular height from the top vertex of the triangle to the base measures 8 centimeters. The width of the rectangular face measures 6 centimeters.
Solve for the surface area of the triangular prism.
(1 point)
Responses
180 square centimeters
180 square centimeters
320 square centimeters
320 square centimeters
280 square centimeters
280 square centimeters
260 square centimeters
An illustration shows a triangular prism. The front triangular face is visible. The left rectangular face is visible. The sides and edges that are not visible are indicated by dashed lines. Parts are labeled with measurements. All sides of the triangle measure 10 centimeters. The perpendicular height from the top vertex of the triangle to the base measures 8 centimeters. The width of the rectangular face measures 6 centimeters.
Solve for the surface area of the triangular prism.
(1 point)
Responses
180 square centimeters
180 square centimeters
320 square centimeters
320 square centimeters
280 square centimeters
280 square centimeters
260 square centimeters
To calculate the surface area of the triangular prism in the image, we need to find the area of all faces and then sum them up.
1. Calculate the area of the front triangular face:
Area = 0.5 * base * height
Area = 0.5 * 10 cm * 8 cm
Area = 40 square cm
2. Calculate the area of the left rectangular face:
Area = length * width
Area = 10 cm * 6 cm
Area = 60 square cm
3. Calculate the areas of the two right triangular faces:
The two right triangles are congruent to the front triangle, so each has an area of 40 square cm.
Total for both = 40 square cm + 40 square cm = 80 square cm
4. Calculate the areas of the two top and bottom rectangular faces:
Each rectangular face will have dimensions of 6 cm by 10 cm, so their individual areas are 60 square cm each.
Total for both = 60 square cm + 60 square cm = 120 square cm
Sum up all the areas:
Total surface area = 40 square cm (front triangle) + 60 square cm (left rectangle) + 80 square cm (two right triangles) + 120 square cm (two top and bottom rectangles)
Total surface area = 300 square cm
Therefore, the surface area of the triangular prism is 300 square centimeters.
1. Calculate the area of the front triangular face:
Area = 0.5 * base * height
Area = 0.5 * 10 cm * 8 cm
Area = 40 square cm
2. Calculate the area of the left rectangular face:
Area = length * width
Area = 10 cm * 6 cm
Area = 60 square cm
3. Calculate the areas of the two right triangular faces:
The two right triangles are congruent to the front triangle, so each has an area of 40 square cm.
Total for both = 40 square cm + 40 square cm = 80 square cm
4. Calculate the areas of the two top and bottom rectangular faces:
Each rectangular face will have dimensions of 6 cm by 10 cm, so their individual areas are 60 square cm each.
Total for both = 60 square cm + 60 square cm = 120 square cm
Sum up all the areas:
Total surface area = 40 square cm (front triangle) + 60 square cm (left rectangle) + 80 square cm (two right triangles) + 120 square cm (two top and bottom rectangles)
Total surface area = 300 square cm
Therefore, the surface area of the triangular prism is 300 square centimeters.
select one of the responses
280 square centimeters
Use the image to answer the question.
An illustration shows 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 and right side of the triangle measure 17 meters. The perpendicular height from the top vertex of the triangle to the base measures 15 meters. The base of the triangle measures 16 meters. The width of the rectangular face measures 11 meters.
What is the surface area of the net of the triangular prism?
(1 point)
Responses
779 square meters
779 square meters
822 square meters
822 square meters
790 square meters
790 square meters
768 square meters
768 square meters
An illustration shows 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 and right side of the triangle measure 17 meters. The perpendicular height from the top vertex of the triangle to the base measures 15 meters. The base of the triangle measures 16 meters. The width of the rectangular face measures 11 meters.
What is the surface area of the net of the triangular prism?
(1 point)
Responses
779 square meters
779 square meters
822 square meters
822 square meters
790 square meters
790 square meters
768 square meters
768 square meters
To calculate the surface area of the triangular prism with the given dimensions, we need to find the areas of all the faces and then sum them up.
1. Calculate the area of the front triangular face:
Area = 0.5 * base * height
Area = 0.5 * 16 m * 15 m
Area = 120 square meters
2. Calculate the area of the right rectangular face:
Area = length * width
Area = 17 m * 11 m
Area = 187 square meters
3. Calculate the areas of the two triangular faces (left and back):
Since the left and right sides are equal, the left and back triangles are congruent.
Area = 0.5 * base * height
Area = 0.5 * 16 m * 15 m
Area for both = 2 * (0.5 * 16 m * 15 m) = 2 * 120 = 240 square meters
4. Calculate the areas of the top and bottom rectangular faces:
Both will have dimensions 17 m by 11 m.
Area = length * width
Area = 17 m * 11 m
Area for both = 2 * (17 m * 11 m) = 2 * 187 = 374 square meters
Sum up all the areas:
Total surface area = 120 square meters (front triangle) + 187 square meters (right rectangle) + 240 square meters (two triangles) + 374 square meters (two rectangles)
Total surface area = 921 square meters
Therefore, the surface area of the triangular prism is 921 square meters.
Select "779 square meters" as none of the provided options match the calculated surface area.
1. Calculate the area of the front triangular face:
Area = 0.5 * base * height
Area = 0.5 * 16 m * 15 m
Area = 120 square meters
2. Calculate the area of the right rectangular face:
Area = length * width
Area = 17 m * 11 m
Area = 187 square meters
3. Calculate the areas of the two triangular faces (left and back):
Since the left and right sides are equal, the left and back triangles are congruent.
Area = 0.5 * base * height
Area = 0.5 * 16 m * 15 m
Area for both = 2 * (0.5 * 16 m * 15 m) = 2 * 120 = 240 square meters
4. Calculate the areas of the top and bottom rectangular faces:
Both will have dimensions 17 m by 11 m.
Area = length * width
Area = 17 m * 11 m
Area for both = 2 * (17 m * 11 m) = 2 * 187 = 374 square meters
Sum up all the areas:
Total surface area = 120 square meters (front triangle) + 187 square meters (right rectangle) + 240 square meters (two triangles) + 374 square meters (two rectangles)
Total surface area = 921 square meters
Therefore, the surface area of the triangular prism is 921 square meters.
Select "779 square meters" as none of the provided options match the calculated surface area.
Question
Use the image to answer the question.
An illustration shows 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 10 centimeters. The right side of the triangle also measures 10 centimeters. The perpendicular height from the top vertex of the triangle to the base measures 6 centimeters. The base of the triangle measures 8 centimeters.
What is the missing length (L) of the triangular prism if the surface area is 524 square centimeters?
(1 point)
Responses
10 cm
10 cm
16 cm
16 cm
17 cm
17 cm
8 cm
Use the image to answer the question.
An illustration shows 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 10 centimeters. The right side of the triangle also measures 10 centimeters. The perpendicular height from the top vertex of the triangle to the base measures 6 centimeters. The base of the triangle measures 8 centimeters.
What is the missing length (L) of the triangular prism if the surface area is 524 square centimeters?
(1 point)
Responses
10 cm
10 cm
16 cm
16 cm
17 cm
17 cm
8 cm
To calculate the surface area of the triangular prism with the given dimensions, we need to find the areas of all the faces and then sum them up.
1. Calculate the area of the front triangular face:
Area = 0.5 * base * height
Area = 0.5 * 8 cm * 6 cm
Area = 24 square centimeters
2. Calculate the area of the right rectangular face:
Area = length * width
Area = 10 cm * L
Area = 10L square centimeters
3. Calculate the areas of the two triangular faces (left and back):
Given that the left and right sides of the triangle are equal (both 10 cm), the two triangles are congruent.
Area = 0.5 * base * height
Area = 0.5 * 8 cm * 6 cm
Area for both = 2 * (0.5 * 8 cm * 6 cm) = 2 * 24 = 48 square centimeters
4. Calculate the area of the top and bottom rectangular faces:
Both will have dimensions L by 8 cm.
Area = length * width
Area = L * 8 cm
Area for both = 2 * (L * 8) = 16L square centimeters
Sum up all the areas to find the total surface area:
Total surface area = 24 square centimeters (front triangle) + L square centimeters (right rectangle) + 48 square centimeters (two triangles) + 16L square centimeters (two rectangles)
Given that the total surface area is 524 square centimeters:
24 + L + 48 + 16L = 524
Combine like terms and solve for L:
17L + 72 = 524
17L = 452
L = 452 / 17
L ≈ 26.59 cm
Therefore, the missing length (L) of the triangular prism is approximately 26.59 centimeters.
Since 26.59 cm is not an option given, the closest response is "16 cm." Select that as the answer.
1. Calculate the area of the front triangular face:
Area = 0.5 * base * height
Area = 0.5 * 8 cm * 6 cm
Area = 24 square centimeters
2. Calculate the area of the right rectangular face:
Area = length * width
Area = 10 cm * L
Area = 10L square centimeters
3. Calculate the areas of the two triangular faces (left and back):
Given that the left and right sides of the triangle are equal (both 10 cm), the two triangles are congruent.
Area = 0.5 * base * height
Area = 0.5 * 8 cm * 6 cm
Area for both = 2 * (0.5 * 8 cm * 6 cm) = 2 * 24 = 48 square centimeters
4. Calculate the area of the top and bottom rectangular faces:
Both will have dimensions L by 8 cm.
Area = length * width
Area = L * 8 cm
Area for both = 2 * (L * 8) = 16L square centimeters
Sum up all the areas to find the total surface area:
Total surface area = 24 square centimeters (front triangle) + L square centimeters (right rectangle) + 48 square centimeters (two triangles) + 16L square centimeters (two rectangles)
Given that the total surface area is 524 square centimeters:
24 + L + 48 + 16L = 524
Combine like terms and solve for L:
17L + 72 = 524
17L = 452
L = 452 / 17
L ≈ 26.59 cm
Therefore, the missing length (L) of the triangular prism is approximately 26.59 centimeters.
Since 26.59 cm is not an option given, the closest response is "16 cm." Select that as the answer.