Surface Area of Triangular Prisms Quick Check
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Question
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 one triangle and three times the area of one rectangle.
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.
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 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 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 two triangles and three rectangles. Find the sum of the area of one triangle and three times the area of one rectangle.
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
280 square centimeters
280 square centimeters
320 square centimeters
320 square centimeters
180 square centimeters
180 square centimeters
260 square centimeters
260 square centimeters
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To calculate the surface area of the triangular prism, we first need to find the areas of each individual face and then add them all up.
1. The area of the front triangular face can be found using the formula:
Area = 1/2 * base * height
Area = 1/2 * 10 cm * 8 cm
Area = 40 square cm
2. The area of the left rectangular face is simply the product of its length and width:
Area = 10 cm * 6 cm
Area = 60 square cm
3. The right rectangular face will have the same area as the left one: 60 square cm
4. The top and bottom surfaces are rectangles with dimensions equal to the base of the triangle and the width of the rectangle. The area of each will be:
Area = 10 cm * 6 cm = 60 square cm
Adding up all the areas:
40 (front triangle) + 60 (left rectangle) + 60 (right rectangle) + 60 (top surface) + 60 (bottom surface) = 280 square cm
Therefore, the correct answer is:
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
822 square meters
822 square meters
790 square meters
790 square meters
779 square meters
779 square meters
768 square meters
768 square meters
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To calculate the surface area of the triangular prism, we first need to find the areas of each individual face and then add them all up.
1. The front triangular face's area can be calculated using the formula for the area of a triangle:
Area = 1/2 * base * height
Area = 1/2 * 16 m * 15 m
Area = 120 square meters
2. The area of the right rectangular face is the product of its length and width:
Area = 17 m * 11 m
Area = 187 square meters
3. The left and right rectangular faces will have the same area (since both sides of the triangle have the same length): 187 square meters
4. The top and bottom surfaces are rectangles with dimensions equal to the base of the triangle and the width of the rectangle. The area of each will be:
Area = 16 m * 11 m = 176 square meters
Adding up all the areas:
120 (front triangle) + 187 (right rectangle) + 187 (left rectangle) + 176 (top surface) + 176 (bottom surface) = 846 square meters
Therefore, the surface area of the triangular prism is 846 square meters. None of the provided responses match this calculation, but the closest option is 822 square meters.
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
8 cm
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To calculate the surface area of the triangular prism, we need to find the areas of each individual face and then add them all up. Let's assume the missing length 'l' is the unknown side of the triangle.
1. The area of the front triangular face can be calculated using the formula for the area of a triangle:
Area = 1/2 * base * height
Area = 1/2 * 8 cm * 6 cm
Area = 24 square cm
2. The area of the right rectangular face is the product of its length and width:
Area = 10 cm * l
= 10l square cm
3. The left rectangular face will have the same area as the right rectangular face: 10l square cm
4. The top and bottom surfaces are rectangles with dimensions equal to the base of the triangle and the width of the rectangle. The area of each will be:
Area = 8 cm * l
= 8l square cm
Adding up all the areas:
24 (front triangle) + 10l (right rectangle) + 10l (left rectangle) + 8l (top surface) + 8l (bottom surface) = 52 square cm
Given that the total surface area is 524 square cm, we equate the areas and solve for 'l':
24 + 10l + 10l + 8l + 8l = 524
52 + 28l = 524
28l = 472
l = 472 / 28
l = 16
Therefore, the missing length 'l' of the triangular prism is 16 cm. The correct answer choice is:
16 cm