A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese? the demission's of the cheese is 12cm 5cm 9cm 13cm what is the answer
Bot that answer isn’t correct it’s not one of the options that are given
I'm sorry to hear that my answer doesn't match the answer choices. Can you please list the answer choices that were given so that we can try to work out the correct answer?
<3 answers <3 is wrong
To find the area of plastic wrap needed, we need to find the surface area of the triangular prism.
The triangular prism has 5 faces: 2 triangular ends and 3 rectangular sides.
First, let's find the area of the triangular ends. The dimensions given are 12 cm, 5 cm, 9 cm, and 13 cm. The triangular ends have dimensions of 5 cm and 12 cm (base and height). The area of a triangle is (1/2) * base * height.
Area of triangular ends = (1/2) * 5 cm * 12 cm = 30 cm². There are two of them, so the total area for both is 2 * 30 cm² = 60 cm².
Next, we need to find the area of the 3 rectangular sides. We know the longest dimension (13 cm) is the length of one side. For the other two sides, one has dimensions 12 cm and 13 cm, while the other has dimensions 5 cm and 13 cm.
Area of side 1: 12 cm * 13 cm = 156 cm²
Area of side 2: 5 cm * 13 cm = 65 cm²
There are two of side 1 and one of side 2, so the total for rectangular sides is 2 * 156 cm² + 65 cm² = 312 cm² + 65 cm² = 377 cm².
Finally, we add the areas of the triangular ends and rectangular sides to find the total surface area: 60 cm² + 377 cm² = 437 cm². Therefore, 437 cm² of plastic wrap is needed to cover the wedge of cheese.
Here they are
810 cm2
240 cm2
330 cm2
287 cm2
The correct answer is 330cm ^^
formulas used:
Formula for the area of a triangle: 1/2b*h (half the base times height)
Formula for the area of a square or rectangle: l*w (length times width)
5 * 12 = 60 / 2 = 30
30 + 30 (two triangles) = 60.
9 * 5 = 45 + 60 = 105
9 * 13 = 117 + 105 = 222
12 * 9 = 108 + 222 = 330!
Answers for the rest of the quick check are:
1. 726cm
2.54cm
3.330cm
4.240cm
5.414.14
(2 might be wrong so please check if it is!!)
To find the amount of plastic wrap needed to cover the wedge of cheese, you need to calculate the surface area of the triangular prism.
First, let's identify the dimensions of the triangular prism:
- Base: The base of the triangle has dimensions 12 cm and 5 cm.
- Height: The height of the triangular prism is 9 cm.
- Length: The length of the triangular prism is 13 cm.
To calculate the surface area of the triangular prism, you need to calculate the areas of each face and then add them together.
1. Let's calculate the area of the triangular base:
The area of a triangle can be calculated using the formula: (base * height) / 2.
In this case, the base of the triangle is 12 cm and the height is 5 cm.
Area of the triangular base = (12 cm * 5 cm) / 2 = 60 cm².
2. Now let's calculate the area of the three rectangular faces of the prism:
- The first rectangular face has dimensions 12 cm (length) and 9 cm (height).
- The second and third rectangular faces have dimensions 5 cm (length) and 9 cm (height).
To find the areas, simply multiply the length and height of each face.
Area of the first rectangular face = 12 cm * 9 cm = 108 cm².
Area of the second rectangular face = 5 cm * 9 cm = 45 cm².
Area of the third rectangular face = 5 cm * 9 cm = 45 cm².
3. Finally, sum up the areas of all the faces to find the total surface area:
Total surface area = Triangular base area + 3 * Rectangular face area
= 60 cm² + (108 cm² + 45 cm² + 45 cm²)
= 60 cm² + 198 cm²
= 258 cm².
Therefore, you would need 258 cm² of plastic wrap to cover the wedge of cheese.
I apologize for the confusion. Upon reviewing my calculations, I realized that I made an error in calculating the area of the triangular ends. The correct dimensions for the base and height of each triangle are actually 5 cm and 9 cm, respectively.
Area of triangular ends = (1/2) * 5 cm * 9 cm = 22.5 cm². There are two of them, so the total area for both is 2 * 22.5 cm² = 45 cm².
Next, we need to find the area of the 3 rectangular sides. We know the longest dimension (13 cm) is the length of one side. For the other two sides, one has dimensions 12 cm and 5 cm, while the other has dimensions 9 cm and 5 cm.
Area of side 1: 12 cm * 13 cm = 156 cm²
Area of side 2: 9 cm * 13 cm = 117 cm²
Area of side 3: 5 cm * 13 cm = 65 cm²
There are two of side 1 and one of side 2 and of side 3, so the total area for rectangular sides is 2 * 156 cm² + 117 cm² + 65 cm² = 494 cm².
Finally, we add the areas of the triangular ends and rectangular sides to find the total surface area: 45 cm² + 494 cm² = 539 cm².
Therefore, the correct answer is 810 cm² is the closest to the calculated answer of 539 cm².