First, calculate the surface area of the box:
- The box has 6 sides, so you need to find the area of each side and then add them all up.
- The top and bottom sides will each have an area of 10 inches x 9 inches = 90 square inches.
- The front and back sides will each have an area of 10 inches x 7 inches = 70 square inches.
- The left and right sides will each have an area of 9 inches x 7 inches = 63 square inches.
Now, add all the areas together:
90 + 90 + 70 + 70 + 63 + 63 = 446 square inches
Since Cherese purchased 500 square inches of cardboard, she will have 500 - 446 = 54 square inches left over.
.Cherese needs to buy some cardboard to build a box 10 inches long, 9 inches wide, and 7 inches high. If she purchases 500 square inches of cardboard, how much will be left over?(1 point)
9 answers
Use the image to answer the question.
An illustration shows a 3 D triangular prism with the triangular face as a right triangle. The edges that are not visible are represented by dashed lines. The length and base of the triangular prism measures 12 centimeters and 9 centimeters. The perpendicular side of the triangular face measures 5 centimeters and the hypotenuse measures 13 centimeters.
A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese?
An illustration shows a 3 D triangular prism with the triangular face as a right triangle. The edges that are not visible are represented by dashed lines. The length and base of the triangular prism measures 12 centimeters and 9 centimeters. The perpendicular side of the triangular face measures 5 centimeters and the hypotenuse measures 13 centimeters.
A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese?
To find the surface area of the triangular prism, we need to calculate the area of each face and add them all together.
1. The triangular face has an area of 1/2 * base * height
Area of the triangular face = 1/2 * 9 cm * 5 cm = 22.5 square centimeters
2. There are two rectangular faces on the sides, each with an area of base * height
Area of each rectangular face = 12 cm * 5 cm = 60 square centimeters
Total area of both rectangular faces = 2 * 60 square centimeters = 120 square centimeters
3. The total surface area of the triangular prism is the sum of all the faces
Total surface area = Triangular face area + 2 * Rectangular face area
Total surface area = 22.5 square cm + 120 square cm = 142.5 square centimeters
Therefore, you will need 142.5 square centimeters of plastic wrap to cover the wedge of cheese.
1. The triangular face has an area of 1/2 * base * height
Area of the triangular face = 1/2 * 9 cm * 5 cm = 22.5 square centimeters
2. There are two rectangular faces on the sides, each with an area of base * height
Area of each rectangular face = 12 cm * 5 cm = 60 square centimeters
Total area of both rectangular faces = 2 * 60 square centimeters = 120 square centimeters
3. The total surface area of the triangular prism is the sum of all the faces
Total surface area = Triangular face area + 2 * Rectangular face area
Total surface area = 22.5 square cm + 120 square cm = 142.5 square centimeters
Therefore, you will need 142.5 square centimeters of plastic wrap to cover the wedge of cheese.
A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese?
To calculate the amount of plastic wrap needed to cover the wedge of cheese, we need to find the surface area of all the faces.
1. The triangular face:
- The base of the triangular prism is 9 centimeters, and the height is 5 centimeters.
- The area of the triangular face is 1/2 * base * height = 1/2 * 9 cm * 5 cm = 22.5 square centimeters.
2. The two rectangular faces:
- The length of the triangle prism is 12 centimeters, and the height is 5 centimeters.
- Each rectangular face has an area of length * height = 12 cm * 5 cm = 60 square centimeters.
- Since there are two rectangular faces, the total area of the two faces is 2 * 60 = 120 square centimeters.
3. Add the areas of all the faces to find the total surface area:
- Total surface area = Triangular face area + 2 * Rectangular face area
- Total surface area = 22.5 square cm + 120 square cm = 142.5 square centimeters.
Therefore, you will need 142.5 square centimeters of plastic wrap to cover the wedge of cheese.
1. The triangular face:
- The base of the triangular prism is 9 centimeters, and the height is 5 centimeters.
- The area of the triangular face is 1/2 * base * height = 1/2 * 9 cm * 5 cm = 22.5 square centimeters.
2. The two rectangular faces:
- The length of the triangle prism is 12 centimeters, and the height is 5 centimeters.
- Each rectangular face has an area of length * height = 12 cm * 5 cm = 60 square centimeters.
- Since there are two rectangular faces, the total area of the two faces is 2 * 60 = 120 square centimeters.
3. Add the areas of all the faces to find the total surface area:
- Total surface area = Triangular face area + 2 * Rectangular face area
- Total surface area = 22.5 square cm + 120 square cm = 142.5 square centimeters.
Therefore, you will need 142.5 square centimeters of plastic wrap to cover the wedge of cheese.
Use the image to answer the question.
An illustration shows a 3 D triangular prism with the triangular face as a right triangle. The edges that are not visible are represented by dashed lines. The length and base of the triangular prism measures 12 centimeters and 9 centimeters. The perpendicular side of the triangular face measures 5 centimeters and the hypotenuse measures 13 centimeters.
A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese?
(1 point)
Responses
330 cm2
330 cm squared
810 cm2
810 cm squared
240 cm2
240 cm squared
287 cm2
An illustration shows a 3 D triangular prism with the triangular face as a right triangle. The edges that are not visible are represented by dashed lines. The length and base of the triangular prism measures 12 centimeters and 9 centimeters. The perpendicular side of the triangular face measures 5 centimeters and the hypotenuse measures 13 centimeters.
A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese?
(1 point)
Responses
330 cm2
330 cm squared
810 cm2
810 cm squared
240 cm2
240 cm squared
287 cm2
To calculate the total surface area of the triangular prism (wedge of cheese) we need to find the areas of all the faces.
1. The triangular face:
The base of the triangular prism (wedge of cheese) is 9 cm and the height is 5 cm.
The area of the triangular face = 1/2 * base * height = 1/2 * 9 cm * 5 cm = 22.5 cm²
2. The two rectangular faces:
The length of the triangular prism (wedge of cheese) is 12 cm and the height is 5 cm.
Each rectangular face has an area of length * height = 12 cm * 5 cm = 60 cm².
Since there are two rectangular faces, the total area of the two faces is 2 * 60 cm² = 120 cm².
Adding all the face areas together, we get:
Total surface area = Triangular face area + 2 * Rectangular face area
Total surface area = 22.5 cm² + 120 cm² = 142.5 cm²
Therefore, the correct answer is:
142.5 cm²
None of the given options are a match for the calculated surface area, so the closest option is 240 cm², but the accurate value is 142.5 cm².
1. The triangular face:
The base of the triangular prism (wedge of cheese) is 9 cm and the height is 5 cm.
The area of the triangular face = 1/2 * base * height = 1/2 * 9 cm * 5 cm = 22.5 cm²
2. The two rectangular faces:
The length of the triangular prism (wedge of cheese) is 12 cm and the height is 5 cm.
Each rectangular face has an area of length * height = 12 cm * 5 cm = 60 cm².
Since there are two rectangular faces, the total area of the two faces is 2 * 60 cm² = 120 cm².
Adding all the face areas together, we get:
Total surface area = Triangular face area + 2 * Rectangular face area
Total surface area = 22.5 cm² + 120 cm² = 142.5 cm²
Therefore, the correct answer is:
142.5 cm²
None of the given options are a match for the calculated surface area, so the closest option is 240 cm², but the accurate value is 142.5 cm².
Use the image to answer the question.
An illustration shows a 3 D triangular prism. The edges that are not visible are represented by dashed lines. The length and base of the triangular prism measures 12 centimeters and 4 centimeters. The perpendicular height h measures 6 centimeters, and the sides of the triangular face measures 7 centimeters.
Jordan purchased a piece of fabric that is 18 cm by 18 cm in order to make a tent for her little sister’s dolls. Using the dimensions for the tent shaped as a triangular prism, how much fabric will be left over?
(1 point)
An illustration shows a 3 D triangular prism. The edges that are not visible are represented by dashed lines. The length and base of the triangular prism measures 12 centimeters and 4 centimeters. The perpendicular height h measures 6 centimeters, and the sides of the triangular face measures 7 centimeters.
Jordan purchased a piece of fabric that is 18 cm by 18 cm in order to make a tent for her little sister’s dolls. Using the dimensions for the tent shaped as a triangular prism, how much fabric will be left over?
(1 point)
To calculate the total surface area of the triangular prism (tent) and determine how much fabric will be left over, we need to find the areas of all the faces.
1. The triangular face:
The base of the triangular prism (tent) is 4 cm and one side of the triangle is 7 cm. To find the height of the triangular face, we can use the Pythagorean theorem:
h² + 4² = 7²
h² + 16 = 49
h² = 33
h ≈ √33 ≈ 5.74 cm
The area of the triangular face = 1/2 * base * height = 1/2 * 4 cm * 5.74 cm ≈ 11.48 cm².
2. The two rectangular faces:
The length of the triangular prism (tent) is 12 cm and the height is 6 cm.
Each rectangular face has an area of length * height = 12 cm * 6 cm = 72 cm².
Since there are two rectangular faces, the total area of the two faces is 2 * 72 cm² = 144 cm².
Adding all the face areas together, we get:
Total surface area = Triangular face area + 2 * Rectangular face area
Total surface area = 11.48 cm² + 144 cm² ≈ 155.48 cm²
Jordan's fabric is 18 cm by 18 cm, which gives a total area of 18 cm * 18 cm = 324 cm².
The fabric needed for the tent is 155.48 cm² and the remaining fabric will be:
324 cm² - 155.48 cm² = 168.52 cm².
Therefore, Jordan will have approximately 168.52 cm² of fabric left over after making the tent for her little sister's dolls.
1. The triangular face:
The base of the triangular prism (tent) is 4 cm and one side of the triangle is 7 cm. To find the height of the triangular face, we can use the Pythagorean theorem:
h² + 4² = 7²
h² + 16 = 49
h² = 33
h ≈ √33 ≈ 5.74 cm
The area of the triangular face = 1/2 * base * height = 1/2 * 4 cm * 5.74 cm ≈ 11.48 cm².
2. The two rectangular faces:
The length of the triangular prism (tent) is 12 cm and the height is 6 cm.
Each rectangular face has an area of length * height = 12 cm * 6 cm = 72 cm².
Since there are two rectangular faces, the total area of the two faces is 2 * 72 cm² = 144 cm².
Adding all the face areas together, we get:
Total surface area = Triangular face area + 2 * Rectangular face area
Total surface area = 11.48 cm² + 144 cm² ≈ 155.48 cm²
Jordan's fabric is 18 cm by 18 cm, which gives a total area of 18 cm * 18 cm = 324 cm².
The fabric needed for the tent is 155.48 cm² and the remaining fabric will be:
324 cm² - 155.48 cm² = 168.52 cm².
Therefore, Jordan will have approximately 168.52 cm² of fabric left over after making the tent for her little sister's dolls.