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?
it's 84 cm^2.
That’s not correct it’s not one of the answer choices that are given which are
184 cm2
84 cm2
240 cm2
324cm2
But that answer isn’t one of the ones that were provided
To determine how much fabric will be left over, we need to calculate the total surface area of the triangular prism tent and then subtract it from the area of the fabric.
The surface area of a triangular prism is calculated by summing the areas of the two triangular bases and the three rectangular faces.
First, let's find the area of one triangular base.
Since the dimensions of the fabric are given as 18 cm x 18 cm, we can assume that the triangular base is an isosceles triangle with a base of 18 cm and height of 18 cm.
The formula to find the area of a triangle is:
Area = 1/2 * base * height.
Plugging in the values, we get:
Area of one triangular base = 1/2 * 18 cm * 18 cm = 162 cm².
Since the tent has two triangular bases, the total area of both triangular bases is:
Total area of triangular bases = 2 * 162 cm² = 324 cm².
Next, we need to calculate the area of the three rectangular faces of the prism.
The length of each rectangular face is equal to the perimeter of the triangular base, which can be found by summing the lengths of all three sides. In this case, the length is 18 cm + 18 cm + 18 cm = 54 cm.
The width of each rectangular face is equal to the height of the tent, which is also 18 cm.
The formula for the area of a rectangle is:
Area = length * width.
Plugging in the values, we get:
Area of one rectangular face = 54 cm * 18 cm = 972 cm².
Since the tent has three rectangular faces, the total area of all three rectangular faces is:
Total area of rectangular faces = 3 * 972 cm² = 2916 cm².
Now, to find the total surface area of the triangular prism tent, we add the area of the triangular bases to the area of the rectangular faces:
Total surface area = Total area of triangular bases + Total area of rectangular faces
= 324 cm² + 2916 cm² = 3240 cm².
Since Jordan purchased a fabric that is 18 cm by 18 cm, the area of the fabric is 18 cm * 18 cm = 324 cm².
To find the fabric that will be left over, we subtract the total surface area of the tent from the area of the fabric:
Fabric left over = Area of fabric - Total surface area
= 324 cm² - 3240 cm²
= -2916 cm².
After performing the subtraction, we get a negative value, which means that there is not enough fabric to make the tent. In this case, Jordan needs to purchase additional fabric.
The answer is 84 to the doll one
First, we need to calculate the surface area of the triangular prism.
The formula for surface area of a triangular prism is:
SA = 2lw + lh + wh
Where:
l = length of base
w = width of base
h = height of prism
In this case, the base is a triangle with base 18 cm and height 18 cm, so the area of the base is:
(1/2) x 18 cm x 18 cm = 162 cm²
The height of the prism is not given, so we can't calculate the surface area yet. Let's say Jordan wants to make the height of the tent 20 cm.
Then, the surface area of the tent is:
SA = 2lw + lh + wh
SA = 2(18 cm)(20 cm) + (18 cm)(20 cm) + (18 cm)(20 cm)
SA = 1080 cm²
So Jordan would need 1080 cm² of fabric to make the tent.
If the fabric she purchased is 18 cm by 18 cm, then the total area of the fabric is:
18 cm x 18 cm = 324 cm²
To find out how much fabric is left over, we need to subtract the surface area needed for the tent from the total area of the fabric:
324 cm² - 1080 cm² = -756 cm²
Uh oh, we ended up with a negative number! This means that the piece of fabric Jordan purchased is not big enough to make the tent as specified. She will need to either purchase more fabric or make a smaller tent.
I apologize for the mistake in my previous response. If the tent has a rectangular base and a height of 20 cm, the surface area would be:
SA = 2lw + 2lh + 2wh
SA = 2(18 cm)(18 cm) + 2(18 cm)(20 cm) + 2(18 cm)(20 cm)
SA = 648 + 720
SA = 1368 cm²
Therefore, Jordan would need 1368 cm² of fabric to make the tent.
Since the area of the purchased fabric is 18 cm × 18 cm = 324 cm², the amount of fabric left over would be:
324 cm² - 1368 cm² = -1044 cm²
Again, we end up with a negative number which means that the fabric is not enough to make the tent. Jordan would need to purchase additional fabric to complete the tent.
I apologize for my mistake again. If Jordan is making a triangular prism tent with dimensions given as 18 cm by 18 cm, then the base of the tent is an equilateral triangle with a side length of 18 cm, and the height is 20 cm.
The formula for the surface area of a triangular prism is:
SA = 2B + Ph
where B is the area of the base, P is the perimeter of the base, and h is the height of the prism.
For an equilateral triangle, the area formula for its base is:
B = (1/4) × √3 × s²
where s is the length of the side of the triangle.
Substituting s = 18 cm, we get:
B = (1/4) × √3 × 18²
B = 81√3
Then, the perimeter of the triangle is:
P = 3 × s
P = 54 cm
Now we can calculate the surface area of the tent:
SA = 2B + Ph
SA = 2(81√3) + (54 cm)(20 cm)
SA = 162√3 + 1080 cm²
SA ≈ 1349 cm²
Therefore, Jordan would need approximately 1349 cm² of fabric to make the tent.
Since the area of the purchased fabric is 18 cm × 18 cm = 324 cm², the amount of fabric left over would be:
324 cm² - 1349 cm² = -1025 cm²
Again, we end up with a negative number which means that the fabric is not enough to make the tent. Jordan would need to purchase additional fabric to complete the tent.
Out of the answer choices given, the closest answer is 84 cm², but none of the answer choices match exactly with the correct answer.