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Original Question
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 dime...Asked by idontgiveaflip
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)
Responses
324 cm2
324 cm squared
240 cm2
240 cm squared
184 cm2
184 cm squared
84 cm2
(1 point)
Responses
324 cm2
324 cm squared
240 cm2
240 cm squared
184 cm2
184 cm squared
84 cm2
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine how much fabric will be left over after making a tent shaped like a triangular prism, we first need to calculate the area of the fabric Jordan purchased and the area of the tent.
First, calculate the area of the fabric:
\[
\text{Area of fabric} = \text{Length} \times \text{Width} = 18 \, \text{cm} \times 18 \, \text{cm} = 324 \, \text{cm}^2.
\]
Next, we need to calculate the area of the tent. The problem does not specify the dimensions of the tent, so we can assume it is formed from a triangular face with a base of 18 cm and a height of 18 cm (to utilize the fabric fully).
The area of a triangle is given by:
\[
\text{Area of triangle} = \frac{1}{2} \times \text{Base} \times \text{Height}
\]
Assuming the triangular face of the tent has a base of 18 cm and a height of 18 cm:
\[
\text{Area of triangle} = \frac{1}{2} \times 18 \, \text{cm} \times 18 \, \text{cm} = \frac{1}{2} \times 324 \, \text{cm}^2 = 162 \, \text{cm}^2.
\]
Assuming that the tent has two triangular faces for the two ends, with the same dimensions (and ignoring the lateral faces for this calculation) gives us a total area for those faces:
\[
\text{Total area of two triangular faces} = 2 \times 162 \, \text{cm}^2 = 324 \, \text{cm}^2.
\]
If the tent has no lateral area or if we consider only the triangular faces, Jordan would use up all the fabric. Therefore, the area of the fabric minus the area used for the tent results in:
\[
\text{Leftover fabric} = \text{Area of fabric} - \text{Area used} = 324 \, \text{cm}^2 - 324 \, \text{cm}^2 = 0 \, \text{cm}^2.
\]
However, if the tent has sides that also use up fabric (which is likely, but not specified), let's just assume she used some fabric but didn't detail the dimensions.
Based on the choices provided and the total fabric used, if we are looking for leftover fabric from making something more elaborate than our simple triangle, it is difficult to evaluate without specific dimensions for actual tent usage.
Given the answer choices:
1. **324 cm²**
2. **240 cm²**
3. **184 cm²**
4. **84 cm²**
I recommend verifying the dimensions given for the tent, as the calculations for a basic triangular prism indicate a certain amount without extra details. It could be reasonable that with triangular faces and a simple setup something like 240 cm² might be used initially.
**However, the calculation I've done indicates there's either no leftover or requires additional dimensions on lateral area. You might have to consider tent usage for certain leftover values indicated. Based on options considering possible tent sides structure, you might be looking toward 240 cm² as a rough makeshift, assuming side areas. Otherwise, there aren't any leftover based on the data specified.**
First, calculate the area of the fabric:
\[
\text{Area of fabric} = \text{Length} \times \text{Width} = 18 \, \text{cm} \times 18 \, \text{cm} = 324 \, \text{cm}^2.
\]
Next, we need to calculate the area of the tent. The problem does not specify the dimensions of the tent, so we can assume it is formed from a triangular face with a base of 18 cm and a height of 18 cm (to utilize the fabric fully).
The area of a triangle is given by:
\[
\text{Area of triangle} = \frac{1}{2} \times \text{Base} \times \text{Height}
\]
Assuming the triangular face of the tent has a base of 18 cm and a height of 18 cm:
\[
\text{Area of triangle} = \frac{1}{2} \times 18 \, \text{cm} \times 18 \, \text{cm} = \frac{1}{2} \times 324 \, \text{cm}^2 = 162 \, \text{cm}^2.
\]
Assuming that the tent has two triangular faces for the two ends, with the same dimensions (and ignoring the lateral faces for this calculation) gives us a total area for those faces:
\[
\text{Total area of two triangular faces} = 2 \times 162 \, \text{cm}^2 = 324 \, \text{cm}^2.
\]
If the tent has no lateral area or if we consider only the triangular faces, Jordan would use up all the fabric. Therefore, the area of the fabric minus the area used for the tent results in:
\[
\text{Leftover fabric} = \text{Area of fabric} - \text{Area used} = 324 \, \text{cm}^2 - 324 \, \text{cm}^2 = 0 \, \text{cm}^2.
\]
However, if the tent has sides that also use up fabric (which is likely, but not specified), let's just assume she used some fabric but didn't detail the dimensions.
Based on the choices provided and the total fabric used, if we are looking for leftover fabric from making something more elaborate than our simple triangle, it is difficult to evaluate without specific dimensions for actual tent usage.
Given the answer choices:
1. **324 cm²**
2. **240 cm²**
3. **184 cm²**
4. **84 cm²**
I recommend verifying the dimensions given for the tent, as the calculations for a basic triangular prism indicate a certain amount without extra details. It could be reasonable that with triangular faces and a simple setup something like 240 cm² might be used initially.
**However, the calculation I've done indicates there's either no leftover or requires additional dimensions on lateral area. You might have to consider tent usage for certain leftover values indicated. Based on options considering possible tent sides structure, you might be looking toward 240 cm² as a rough makeshift, assuming side areas. Otherwise, there aren't any leftover based on the data specified.**
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