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?

Answer 1

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.

Answer 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

Answer 3

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.

Answer 4

But that answer isn’t one of the ones that were provided

Answer 5

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.

Answer 6

it's 84 cm^2.

Answer 7

The answer is 84 to the doll one